A009290 Expansion of exp(x)/cos(sinh(x)).

1, 1, 2, 4, 16, 56, 328, 1576, 12160, 74944, 721280, 5428864, 62638720, 556999808, 7495723264, 76901598208, 1182630301696, 13750425100288, 237887012458496, 3091282934198272, 59422015832915968, 853453694386847744

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) ~ n! * (1 + (-1)^n + (1-(-1)^n)*Pi / sqrt(4+Pi^2)) / (log((Pi + sqrt(4 + Pi^2))/2))^(n+1). - Vaclav Kotesovec, Jan 22 2015

Mathematica

Exp[ x ]/Cos[ Sinh[ x ] ]
CoefficientList[Series[E^x*Sec[Sinh[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

Crossrefs

Sequence in context: A068789 A009624 A009161 * A235459 A081919 A362524

Adjacent sequences: A009287 A009288 A009289 * A009291 A009292 A009293

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Status

approved