A292840 Number of sets of nonempty words with a total of n letters over 6-ary alphabet.

1, 6, 51, 452, 3777, 31074, 250735, 1993176, 15640983, 121378650, 932738805, 7105552308, 53709133137, 403124780178, 3006420386499, 22290321581448, 164378277308862, 1206180958964508, 8810022165617086, 64073173243207632, 464122836576398454, 3349321050668452460

Offset: 0

Author

Alois P. Heinz, Sep 24 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=6 of A292804.

Programs

Maple

h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1)*binomial(6^i, j), j=0..n/i)))
    end:
a:= n-> h(n$2):
seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} (1+x^j)^(6^j).

a(n) ~ 6^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(6^(m-1)-1)) = 0.091503304254691843343610606469481430508... - Vaclav Kotesovec, Sep 28 2017