A316158 Expansion of e.g.f. exp(exp(exp(x*exp(x)) - 1) - 1).

1, 1, 5, 33, 280, 2883, 34817, 481477, 7489454, 129259662, 2448516959, 50460561330, 1123192711285, 26838555204646, 684871918806173, 18580595826856937, 533846105922876855, 16187892824592956798, 516492582419620294678, 17292646954057122160416, 606075769032914504000388

Offset: 0

Author

Ilya Gutkovskiy, Jun 25 2018

Keywords

• nonn

Comments

Natural numbers exponentiated thrice.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..423
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000248, A000258, A007550.

Programs

Maple

a:= (proc(p) local g; g:= proc(n) option remember; `if`(n=0, 1,
       p(n)+add(binomial(n-1, k-1)*p(k)*g(n-k), k=1..n-1))
     end end@@3)(j-> j):
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 25 2018

Mathematica

nmax = 20; CoefficientList[Series[Exp[Exp[Exp[x Exp[x]] - 1] - 1], {x, 0, nmax}], x] Range[0, nmax]!
b[n_] := b[n] = Sum[k^(n - k) Binomial[n, k] BellB[k], {k, n}]; a[n_] := a[n] = Sum[b[k] Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 20}]