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

0,4

Comments

Stirling transform of A005046 (with interpolated zeros).

Exponential transform of A024430.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..485

Formula

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

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]!

Crossrefs

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

Sequence in context: A091845 A020061 A370514 * A125696 A001776 A261001

Adjacent sequences: A330038 A330039 A330040 * A330042 A330043 A330044

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 28 2019

Status

approved