OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..381
FORMULA
a(n) = [x^n] Product_{j=1..n} (1+x^j)^(n^j).
a(n) ~ n^(n - 3/4) * exp(2*sqrt(n) - 1/2) / (2*sqrt(Pi)). - Vaclav Kotesovec, Aug 26 2019
EXAMPLE
a(0) = 1: {}.
a(1) = 1: {a}.
a(2) = 5: {aa}, {ab}, {ba}, {bb}, {a,b}.
MAPLE
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))
end:
a:= n-> h(n$3):
seq(a(n), n=0..20);
MATHEMATICA
h[n_, i_, k_] := h[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[h[n - i*j, i - 1, k]*Binomial[k^i, j], {j, 0, n/i}]]];
a[n_] := h[n, n, n];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 04 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 23 2017
STATUS
approved