cp's OEIS Frontend

A340417 Number of sets of nonempty words with a total of n letters over denary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340417 #5 Jan 07 2021 17:04:30
%S A340417 1,1,3,13,60,326,2065,14508,116845,1039459,10339365,72459687,
%T A340417 581246095,4483235005,36697945720,298344453071,2601248199787,
%U A340417 22469318990159,208007606797845,1867498245975013,17978675539264085,153181998023380623,1392447676785436846
%N A340417 Number of sets of nonempty words with a total of n letters over denary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340417 Alois P. Heinz, <a href="/A340417/b340417.txt">Table of n, a(n) for n = 0..1000</a>
%F A340417 G.f.: Product_{j>=1} (1+x^j)^A226880(j).
%p A340417 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340417       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340417     end:
%p A340417 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340417 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340417       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340417     end:
%p A340417 a:= n-> h(n$2, min(n, 10)):
%p A340417 seq(a(n), n=0..32);
%Y A340417 Column k=10 of A292795.
%Y A340417 Cf. A226880.
%K A340417 nonn
%O A340417 0,3
%A A340417 _Alois P. Heinz_, Jan 07 2021