A323672 Expansion of e.g.f. exp(exp(x)*BesselI(1,2*x)/x - 1).

1, 1, 3, 11, 50, 267, 1633, 11195, 84745, 700332, 6262087, 60146704, 616841371, 6720592647, 77453291594, 940701503518, 12001369992614, 160373548837863, 2238995849944224, 32584082576638311, 493289434851850445, 7754247825363510168, 126354223534523911670, 2131014061115010861375

Offset: 0

Author

Ilya Gutkovskiy, Jan 23 2019

Keywords

• nonn

Crossrefs

Cf. A001006, A304788.

Programs

Maple

seq(n!*coeff(series(exp(exp(x)*BesselI(1,2*x)/x-1),x=0,24),x,n), n=0..23); # Paolo P. Lava, Jan 28 2019

Mathematica

nmax = 23; CoefficientList[Series[Exp[Exp[x] BesselI[1, 2 x]/x - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Hypergeometric2F1[(1 - k)/2, -k/2, 2, 4] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A001006(k)*binomial(n-1,k-1)*a(n-k).