A009124 Expansion of e.g.f. cosh(log(1+sinh(x))).

1, 0, 1, -3, 16, -90, 616, -4893, 44416, -453540, 5145856, -64222983, 874402816, -12897183390, 204862698496, -3486535686273, 63292764553216, -1220795601029640, 24931903045697536, -537463528325234763

Offset

0,4

Links

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

Formula

a(2*n) = A006154(2*n)/2, n>0. - Ralf Stephan, Apr 29 2004

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

Mathematica

CoefficientList[Series[(1 + (1 + Sinh[x])^2)/(2*(1 + Sinh[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+sinh(x))))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Sinh(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

Crossrefs

Sequence in context: A074562 A130744 A344455 * A067679 A099952 A305852

Adjacent sequences: A009121 A009122 A009123 * A009125 A009126 A009127

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved