A009122 - OEIS

%I #19 Sep 08 2022 08:44:37

%S 1,0,1,-6,41,-335,3229,-36036,457932,-6534384,103499016,-1802302128,

%T 34227784920,-704076488232,15595687319640,-370108332316992,

%U 9368461983616128,-251958336139856448,7174771808983995456

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

%H G. C. Greubel, <a href="/A009122/b009122.txt">Table of n, a(n) for n = 0..250</a>

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

%t CoefficientList[Series[(1 + (1 + Log[1 + x])^2)/(2*(1 + Log[1 + 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+log(1+x))))) \\ _G. C. Greubel_, Jul 26 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+Log(1+x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 26 2018

%Y Twice the absolute values are in A052864.

%K sign,easy

%O 0,4

%A _R. H. Hardin_

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