OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 23 2019
STATUS
approved