cp's OEIS Frontend

A340416 Number of sets of nonempty words with a total of n letters over nonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340416 #6 Jan 07 2021 16:45:43
%S A340416 1,1,3,13,60,326,2065,14508,116845,1039459,6710565,48872487,350817295,
%T A340416 2619846205,20019859960,158415989711,1300359929707,10644485545679,
%U A340416 91963547963925,715052566412773,5842504427274965,47435773495721103,390005026265914606,3225674439739003413
%N A340416 Number of sets of nonempty words with a total of n letters over nonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340416 Alois P. Heinz, <a href="/A340416/b340416.txt">Table of n, a(n) for n = 0..1000</a>
%F A340416 G.f.: Product_{j>=1} (1+x^j)^A226879(j).
%p A340416 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340416       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340416     end:
%p A340416 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340416 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340416       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340416     end:
%p A340416 a:= n-> h(n$2, min(n, 9)):
%p A340416 seq(a(n), n=0..32);
%Y A340416 Column k=9 of A292795.
%Y A340416 Cf. A226879.
%K A340416 nonn
%O A340416 0,3
%A A340416 _Alois P. Heinz_, Jan 07 2021