A292841 Number of sets of nonempty words with a total of n letters over 7-ary alphabet.

1, 7, 70, 721, 7042, 67592, 636517, 5904746, 54072137, 489655873, 4390760297, 39030158111, 344244293260, 3014869505704, 26235190722937, 226961433002801, 1952889252127030, 16720135949099562, 142493658202081151, 1209158776638832488, 10219419639669800154

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=7 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(7^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)^(7^j).

a(n) ~ 7^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(7^(m-1)-1)) = 0.07704538722753681799661640414751144459... - Vaclav Kotesovec, Sep 28 2017