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A287317 a(n) = (2*n)! [x^n] BesselI(0, 2*sqrt(x))^5. 3
1, 10, 270, 10900, 551950, 32232060, 2070891900, 142317232200, 10277494548750, 770878551371500, 59577647564312020, 4717432065143561400, 381091087190569291900, 31308955091335405435000, 2609450031306515140215000, 220199552765301571338488400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) = binomial(2*n,n)*A169714(n).

a(n) ~ 2^(2*n) * 5^(2*n + 5/2) / (16 * Pi^(5/2) * n^(5/2)). - Vaclav Kotesovec, Nov 13 2017

MAPLE

A287317_list := proc(len) series(BesselI(0, 2*sqrt(x))^5, x, len);

seq((2*i)!*coeff(%, x, i), i=0..len-1) end: A287317_list(16);

MATHEMATICA

Table[SeriesCoefficient[BesselI[0, 2 Sqrt[x]]^5, {x, 0, n}] (2 n) !, {n, 0, 15}]

Table[Binomial[2n, n]^2 Sum[(Binomial[n, j]^4/Binomial[2n, 2j]) HypergeometricPFQ[{-j, -j, -j}, {1, 1/2-j}, 1/4], {j, 0, n}], {n, 0, 15}]

CROSSREFS

Case k=5 of A287318.

Cf. A169714, A287316.

Sequence in context: A166811 A089906 A294515 * A084943 A055055 A222998

Adjacent sequences:  A287314 A287315 A287316 * A287318 A287319 A287320

KEYWORD

nonn

AUTHOR

Peter Luschny, May 23 2017

STATUS

approved

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Last modified January 21 05:57 EST 2022. Contains 350473 sequences. (Running on oeis4.)