A292844 Number of sets of nonempty words with a total of n letters over 10-ary alphabet.

1, 10, 145, 2120, 29660, 406752, 5475160, 72591320, 950032770, 12294612660, 157545928646, 2001232474600, 25222164942650, 315640538122100, 3924720693484450, 48514280936275240, 596460638741281825, 7296675024124004450, 88849865885787401525, 1077249149081661058800

Offset: 0

Author

Alois P. Heinz, Sep 24 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..975

Crossrefs

Column k=10 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(10^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)^(10^j).

a(n) ~ 10^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(10^(m-1)-1)) = 0.05242033574521236673164923513877706425... - Vaclav Kotesovec, Sep 28 2017