A330041 - OEIS

%I #8 Jun 23 2023 18:28:45

%S 1,0,1,3,11,55,322,2114,15556,127005,1135374,11011220,115080825,

%T 1288589757,15379512670,194796087841,2608470709562,36805935282625,

%U 545626818921885,8475730766054047,137637670315066835,2331584745107027528,41122505417366272200

%N Expansion of e.g.f. exp(cosh(exp(x) - 1) - 1).

%C Stirling transform of A005046 (with interpolated zeros).

%C Exponential transform of A024430.

%H Alois P. Heinz, <a href="/A330041/b330041.txt">Table of n, a(n) for n = 0..485</a>

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A024430(k) * a(n-k).

%p g:= proc(n) option remember; `if`(n=0, 1, add(

%p       binomial(2*n-1, 2*k-1) *g(n-k), k=1..n))

%p     end:

%p b:= proc(n, m) option remember; `if`(n=0,

%p      `if`(m::odd, 0, g(m/2)), m*b(n-1, m)+b(n-1, m+1))

%p     end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=0..22);  # _Alois P. Heinz_, Jun 23 2023

%t nmax = 22; CoefficientList[Series[Exp[Cosh[Exp[x] - 1] - 1], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A000258, A005046, A024430, A185369, A330021.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Nov 28 2019