OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A002426(k)*binomial(n-1,k-1)*a(n-k).
MAPLE
seq(n!*coeff(series(exp(exp(x)*BesselI(0, 2*x)-1), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 28 2019
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[Exp[x] BesselI[0, 2 x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[3^k Hypergeometric2F1[1/2, -k, 1, 4/3] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 22}]
PROG
(PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(exp(x)*besseli(0, 2*x) - 1))) \\ Michel Marcus, Jan 24 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 23 2019
STATUS
approved