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A336636 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x))^3 - 1). 2
1, 3, 33, 660, 20817, 935388, 56149098, 4311694467, 410200118577, 47174279349540, 6431874002292978, 1023398757621960327, 187566773426941146498, 39164789611542644630415, 9229712819952662426436507, 2435069724188535096598261305 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * A002893(k) * k * a(n-k).

MATHEMATICA

nmax = 15; CoefficientList[Series[Exp[BesselI[0, 2 Sqrt[x]]^3 - 1], {x, 0, nmax}], x] Range[0, nmax]!^2

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 HypergeometricPFQ[{1/2, -k, -k}, {1, 1}, 4] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]

CROSSREFS

Cf. A002893, A023998, A247452, A336635, A336637.

Sequence in context: A002916 A009659 A144756 * A340971 A326328 A233319

Adjacent sequences: A336633 A336634 A336635 * A336637 A336638 A336639

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 28 2020

STATUS

approved

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Last modified January 30 12:56 EST 2023. Contains 359945 sequences. (Running on oeis4.)