login
A009124
Expansion of e.g.f. cosh(log(1+sinh(x))).
1
1, 0, 1, -3, 16, -90, 616, -4893, 44416, -453540, 5145856, -64222983, 874402816, -12897183390, 204862698496, -3486535686273, 63292764553216, -1220795601029640, 24931903045697536, -537463528325234763
OFFSET
0,4
LINKS
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
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved