A235134 E.g.f. 1/(1 - sinh(2*x))^(1/2).

1, 1, 3, 19, 153, 1561, 19563, 289339, 4932273, 95258161, 2055639123, 49019157859, 1280056939593, 36329281202761, 1113449691889083, 36651273215389579, 1289577677407798113, 48299079453732363361, 1918528841276621473443, 80559757274836073592499

Offset

0,3

Comments

Generally, for e.g.f. 1/(1-sinh(p*x))^(1/p) we have a(n) ~ n! * p^n / (Gamma(1/p) * 2^(1/(2*p)) * n^(1-1/p) * (arcsinh(1))^(n+1/p)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..395

Formula

a(n) ~ n! * 2^(n-1/4) / (sqrt(Pi*n) * (log(1+sqrt(2)))^(n+1/2)).

Mathematica

CoefficientList[Series[1/(1-Sinh[2*x])^(1/2), {x, 0, 20}], x] * Range[0, 20]!

Prog

(PARI) x='x+O('x^50); Vec(serlaplace(1/(sqrt(1-sinh(2*x))))) \\ G. C. Greubel, Apr 05 2017

Crossrefs

Cf. A235135, A001586, A235131.

Sequence in context: A113013 A307489 A323668 * A235322 A105784 A077046

Adjacent sequences: A235131 A235132 A235133 * A235135 A235136 A235137

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 03 2014

Status

approved