A009131 Expansion of e.g.f. cosh(log(1+x))/cosh(x).

1, 0, 0, -3, 11, -30, 194, -1785, 13957, -113148, 1143284, -13131855, 156950639, -2005222362, 28119703702, -424785970245, 6792043718345, -115135087505400, 2072993596779944, -39432571052652315, 788564865102950035

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

a(n) ~ n! * (-1)^n / (exp(1) + exp(-1)). - Vaclav Kotesovec, Jan 22 2015

Mathematica

CoefficientList[Series[((1 + (1 + x)^2)*Sech[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 22 2015 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x))/cosh(x))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x))/Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

Crossrefs

Sequence in context: A330148 A085376 A196233 * A003554 A003523 A018781

Adjacent sequences: A009128 A009129 A009130 * A009132 A009133 A009134

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved