A009294 Expansion of e.g.f.: exp(x)/cosh(log(1+x)).

1, 1, 0, 1, 1, -9, 46, -125, -279, 7021, -57644, 247941, 829225, -30119309, 346210866, -2030635529, -9055135439, 430103734425, -6356431497464, 47224459865161, 263232787214961, -15445025103197969, 278983778423699350

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

J. Cigler, Some remarks about q-Chebyshev polynomials and q-Catalan numbers and related results, arXiv:1312.2767 [math.CO], 2013.

Formula

a(n) ~ n! * sqrt(2) * cos(1-(3*n-1)*(Pi/4)) / (2^(n/2) * exp(1)). - Vaclav Kotesovec, Jan 24 2015

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x]/Cosh[Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 27 2013 *)
CoefficientList[Series[(2*E^x*(1 + x))/(1 + (1 + x)^2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

Crossrefs

Sequence in context: A117052 A356424 A280852 * A061620 A260513 A001781

Adjacent sequences: A009291 A009292 A009293 * A009295 A009296 A009297

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Aug 27 2013

Status

approved