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A330041 Expansion of e.g.f. exp(cosh(exp(x) - 1) - 1).

%I A330041 #8 Jun 23 2023 18:28:45
%S A330041 1,0,1,3,11,55,322,2114,15556,127005,1135374,11011220,115080825,
%T A330041 1288589757,15379512670,194796087841,2608470709562,36805935282625,
%U A330041 545626818921885,8475730766054047,137637670315066835,2331584745107027528,41122505417366272200
%N A330041 Expansion of e.g.f. exp(cosh(exp(x) - 1) - 1).
%C A330041 Stirling transform of A005046 (with interpolated zeros).
%C A330041 Exponential transform of A024430.
%H A330041 Alois P. Heinz, <a href="/A330041/b330041.txt">Table of n, a(n) for n = 0..485</a>
%F A330041 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A024430(k) * a(n-k).
%p A330041 g:= proc(n) option remember; `if`(n=0, 1, add(
%p A330041       binomial(2*n-1, 2*k-1) *g(n-k), k=1..n))
%p A330041     end:
%p A330041 b:= proc(n, m) option remember; `if`(n=0,
%p A330041      `if`(m::odd, 0, g(m/2)), m*b(n-1, m)+b(n-1, m+1))
%p A330041     end:
%p A330041 a:= n-> b(n, 0):
%p A330041 seq(a(n), n=0..22);  # _Alois P. Heinz_, Jun 23 2023
%t A330041 nmax = 22; CoefficientList[Series[Exp[Cosh[Exp[x] - 1] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%Y A330041 Cf. A000258, A005046, A024430, A185369, A330021.
%K A330041 nonn
%O A330041 0,4
%A A330041 _Ilya Gutkovskiy_, Nov 28 2019