cp's OEIS Frontend

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

%I A292844 #7 Sep 28 2017 04:31:36
%S A292844 1,10,145,2120,29660,406752,5475160,72591320,950032770,12294612660,
%T A292844 157545928646,2001232474600,25222164942650,315640538122100,
%U A292844 3924720693484450,48514280936275240,596460638741281825,7296675024124004450,88849865885787401525,1077249149081661058800
%N A292844 Number of sets of nonempty words with a total of n letters over 10-ary alphabet.
%H A292844 Alois P. Heinz, <a href="/A292844/b292844.txt">Table of n, a(n) for n = 0..975</a>
%F A292844 G.f.: Product_{j>=1} (1+x^j)^(10^j).
%F A292844 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
%p A292844 h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A292844       add(h(n-i*j, i-1)*binomial(10^i, j), j=0..n/i)))
%p A292844     end:
%p A292844 a:= n-> h(n$2):
%p A292844 seq(a(n), n=0..30);
%Y A292844 Column k=10 of A292804.
%K A292844 nonn
%O A292844 0,2
%A A292844 _Alois P. Heinz_, Sep 24 2017