OFFSET
0,3
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
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 25 2018
STATUS
approved