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

0,2

Links

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

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

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);

Crossrefs

Column k=7 of A292804.

Sequence in context: A196662 A249750 A144848 * A180902 A078246 A268301

Adjacent sequences: A292838 A292839 A292840 * A292842 A292843 A292844

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2017

Status

approved