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

0,2

Links

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

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

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);

Crossrefs

Column k=6 of A292804.

Sequence in context: A372731 A050916 A011790 * A356394 A202754 A363112

Adjacent sequences: A292837 A292838 A292839 * A292841 A292842 A292843

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2017

Status

approved