OFFSET
0,4
COMMENTS
E.g.f. is inverse of e.g.f. for A001006 (Motzkin numbers).
FORMULA
E.g.f.: 1 / Sum_{k>=0} A001006(k)*x^k/k!.
MATHEMATICA
nmax = 26; CoefficientList[Series[x Exp[-x]/BesselI[1, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] Hypergeometric2F1[(1 - k)/2, -k/2, 2, 4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 26}]
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(-x) / besseli(1, 2*x))) \\ Michel Marcus, Jul 02 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 28 2019
STATUS
approved