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A308848 Expansion of e.g.f. exp(-x) / BesselI(0,2*x). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..24.

FORMULA

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

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}]

PROG

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

CROSSREFS

Cf. A002426, A167022, A308847.

Sequence in context: A073624 A025546 A308397 * A109715 A128465 A098967

Adjacent sequences:  A308845 A308846 A308847 * A308849 A308850 A308851

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 28 2019

STATUS

approved

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Last modified May 16 12:30 EDT 2021. Contains 343947 sequences. (Running on oeis4.)