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A116385
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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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3
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0, 0, 1, 2, 5, 10, 21, 42, 84, 168, 330, 660, 1287, 2574, 5005, 10010, 19448, 38896, 75582, 151164, 293930, 587860, 1144066, 2288132, 4457400, 8914800, 17383860, 34767720, 67863915, 135727830, 265182525, 530365050, 1037158320, 2074316640
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OFFSET
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0,4
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COMMENTS
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Third column of the Riordan array A116382.
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LINKS
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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).
Conjecture: (n+4)*a(n) -2*a(n-1) +(-7*n-8)*a(n-2) +6*a(n-3) +12*(n-2)*a(n-4)=0. - R. J. Mathar, Jun 13 2014
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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MATHEMATICA
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With[{nn=40}, CoefficientList[Series[BesselI[2, 2x]+2BesselI[3, 2x]+ BesselI[ 4, 2x], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Sep 14 2011 *)
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PROG
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(Haskell)
a116385 n = a051631 (n+1) $ (n+1) `div` 2
(PARI) a(n)= binomial(n+3, (n+3)\2) - 3*binomial(n+1, (n+1)\2) \\ Bill McEachen, Dec 12 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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