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

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

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}]

Crossrefs

Cf. A001006, A304788.

Sequence in context: A024334 A162477 A115081 * A103466 A346762 A354323

Adjacent sequences: A323669 A323670 A323671 * A323673 A323674 A323675

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 23 2019

Status

approved