A330041 Expansion of e.g.f. exp(cosh(exp(x) - 1) - 1).
1, 0, 1, 3, 11, 55, 322, 2114, 15556, 127005, 1135374, 11011220, 115080825, 1288589757, 15379512670, 194796087841, 2608470709562, 36805935282625, 545626818921885, 8475730766054047, 137637670315066835, 2331584745107027528, 41122505417366272200
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..485
Programs
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Maple
g:= proc(n) option remember; `if`(n=0, 1, add( binomial(2*n-1, 2*k-1) *g(n-k), k=1..n)) end: b:= proc(n, m) option remember; `if`(n=0, `if`(m::odd, 0, g(m/2)), m*b(n-1, m)+b(n-1, m+1)) end: a:= n-> b(n, 0): seq(a(n), n=0..22); # Alois P. Heinz, Jun 23 2023 -
Mathematica
nmax = 22; CoefficientList[Series[Exp[Cosh[Exp[x] - 1] - 1], {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A024430(k) * a(n-k).
Comments