A308848 Expansion of e.g.f. exp(-x) / BesselI(0,2*x).

1, -1, -1, 5, 7, -71, -139, 2071, 5335, -103207, -331511, 7853251, 30256381, -847377805, -3808492297, 123081031165, 632196102455, -23155450005175, -133802756269735, 5477371955388355, 35167483918412257, -1591161899246627297, -11237664710770159597, 556875003328690925825, 4290500676272573740429

Offset: 0

Author

Ilya Gutkovskiy, Jun 28 2019

Keywords

• sign

Comments

E.g.f. is inverse of e.g.f. for A002426 (central trinomial coefficients).

Crossrefs

Cf. A002426, A167022, A308847.

Programs

Mathematica

nmax = 24; CoefficientList[Series[Exp[-x]/BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] 3^k Hypergeometric2F1[1/2, -k, 1, 4/3] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(-x) / besseli(0,2*x))) \\ Michel Marcus, Jul 02 2019

Formula

E.g.f.: 1 / Sum_{k>=0} A002426(k)*x^k/k!.