A009124 - OEIS

%I #20 Sep 08 2022 08:44:37

%S 1,0,1,-3,16,-90,616,-4893,44416,-453540,5145856,-64222983,874402816,

%T -12897183390,204862698496,-3486535686273,63292764553216,

%U -1220795601029640,24931903045697536,-537463528325234763

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

%H G. C. Greubel, <a href="/A009124/b009124.txt">Table of n, a(n) for n = 0..250</a>

%F a(2*n) = A006154(2*n)/2, n>0. - _Ralf Stephan_, Apr 29 2004

%F a(n) ~ n! * (-1)^n / (2 * sqrt(2) * (log(1+sqrt(2)))^(n+1)). - _Vaclav Kotesovec_, Jan 22 2015

%t CoefficientList[Series[(1 + (1 + Sinh[x])^2)/(2*(1 + Sinh[x])), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 22 2015 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+sinh(x))))) \\ _G. C. Greubel_, Jul 28 2018

%o (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

%K sign,easy

%O 0,4

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997