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#12 by Vaclav Kotesovec at Fri Feb 06 09:32:25 EST 2015
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#11 by Vaclav Kotesovec at Fri Feb 06 09:32:13 EST 2015
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| FORMULA
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a(n) ~ 2*cos(r) * ( * (2*n)! / ((arcsin(r)/cosPi/sin(2*r) + sintan(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.925530521691094119047741289850... is the root of the equation tan(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015
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Discussion
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| Fri Feb 06
| 09:32
| Vaclav Kotesovec: Simplified.
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#10 by Vaclav Kotesovec at Fri Feb 06 09:07:51 EST 2015
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| FORMULA
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a(n) ~ 2*cos(r) * (sin(arcsin(r)*tan(r)))^2 * (2*n)! / ((arcsin(r)/cos(r) + sin(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.925530521691094119047741289850... is the root of the equation tan(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015
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| STATUS
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approved
editing
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#9 by Vaclav Kotesovec at Fri Feb 06 08:45:47 EST 2015
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#8 by Vaclav Kotesovec at Fri Feb 06 08:44:45 EST 2015
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| FORMULA
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a(n) ~ 2*cos(r) * (sin(arcsin(r)*tan(r)))^2 * (2*n)! / ((arcsin(r)/cos(r) + sin(r)/sqrt(1-r^2)) * r^(2*n+1)), where r = 0.925530521691094119047741289850... is the root of the equation tan(r)*arcsin(r) = Pi/2. - Vaclav Kotesovec, Feb 06 2015
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#7 by Vaclav Kotesovec at Fri Feb 06 08:30:40 EST 2015
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| LINKS
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Vaclav Kotesovec, <a href="/A012378/b012378.txt">Table of n, a(n) for n = 0..220</a>
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#6 by Vaclav Kotesovec at Fri Feb 06 08:05:08 EST 2015
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| MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[Tan[ArcSin[x]*Tan[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)
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#5 by Vaclav Kotesovec at Fri Feb 06 03:30:01 EST 2015
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| DATA
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0, 2, 12, 430, 26040, 2661178, 402231940, 84456360742, 23476965450736, 8341678414816242, 3686586514781799292, 1982979948714026781726, 1275341677617693817452200, 966341800352400737116306986
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| OFFSET
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0,12
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| EXTENSIONS
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a(0)=0 prepended by Vaclav Kotesovec, Feb 06 2015
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| STATUS
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approved
editing
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#4 by Charles R Greathouse IV at Fri Feb 24 12:50:48 EST 2012
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| AUTHOR
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Patrick Demichel (dmlpatrick.demichel(AT)hpfrcu03.france.hp.com)
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Discussion
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| Fri Feb 24
| 12:50
| OEIS Server: https://oeis.org/edit/global/108
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#3 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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Patrick Demichel (dml@(AT)hpfrcu03.france.hp.com)
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