A336636 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x))^3 - 1).

1, 3, 33, 660, 20817, 935388, 56149098, 4311694467, 410200118577, 47174279349540, 6431874002292978, 1023398757621960327, 187566773426941146498, 39164789611542644630415, 9229712819952662426436507, 2435069724188535096598261305

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: A144756 A377453 A377446 * A364242 A376390 A376393

Adjacent sequences: A336633 A336634 A336635 * A336637 A336638 A336639

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 28 2020

Status

approved