OFFSET
0,2
COMMENTS
E.g.f. is inverse of e.g.f. for A000984 (central binomial coefficients).
FORMULA
E.g.f.: 1 / Sum_{k>=0} binomial(2*k,k)*x^k/k!.
MATHEMATICA
nmax = 24; CoefficientList[Series[Exp[-2 x]/BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] Binomial[2 k, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(-2*x) / besseli(0, 2*x))) \\ Michel Marcus, Jul 02 2019
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 28 2019
STATUS
approved