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#31 by Michael De Vlieger at Mon Oct 09 09:25:01 EDT 2023
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#30 by Michel Marcus at Mon Oct 09 05:47:06 EDT 2023
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#29 by Gennady Eremin at Mon Oct 09 04:17:00 EDT 2023
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#28 by Gennady Eremin at Mon Oct 09 04:15:29 EDT 2023
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| FORMULA
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G.f.: (-1 - x + x^2 + B(x) - 3*x^2*B(x))/x^3, where B(x) is the g.f. of A001405. - Gennady Eremin, Oct 09 2023
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approved
editing
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#27 by Sean A. Irvine at Sun Jan 08 14:45:17 EST 2023
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#26 by Michel Marcus at Sat Dec 17 08:39:51 EST 2022
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#25 by Michel Marcus at Sat Dec 17 08:39:46 EST 2022
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| FORMULA
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E.g.f.: (d/dx)(Bessel_I(3,2x),x) + 2*Bessel_I(3,2x); a(n) = C(n+1,floor((n-2)/2)*(1+(-1)^n)/2 + C(n,floor((n-3)/2))*(1-(-1)^n).
a(n) = C(n+1,floor((n-2)/2)*(1+(-1)^n)/2 + C(n,floor((n-3)/2))*(1-(-1)^n).
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proposed
editing
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#24 by Jon E. Schoenfield at Fri Dec 16 03:09:17 EST 2022
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#23 by Jon E. Schoenfield at Fri Dec 16 03:09:15 EST 2022
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Expansion of e.g.f. Bessel_I(2,2x)+) + 2*Bessel_I(3,2x)+) + Bessel_I(4,2x).
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| COMMENTS
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Apart from its root term -1: central terms of the triangle in A051631: a(n) = A051631(n+1, [(n+1)/2]). [_]). - _Reinhard Zumkeller_, Nov 13 2011]
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E.g.f.: dif(.: (d/dx)(Bessel_I(3,2x),x)+) + 2*Bessel_I(3,2x); a(n)=) = C(n+1,floor((n-2)/2)()*(1+(-1)^n)/2+ + C(n,floor((n-3)/2))())*(1-(-1)^n).
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proposed
editing
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#22 by Bill McEachen at Tue Dec 13 11:24:53 EST 2022
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