cp's OEIS Frontend

A340410 Number of sets of nonempty words with a total of n letters over ternary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340410 #6 Jan 06 2021 19:43:32
%S A340410 1,1,3,13,36,122,433,1356,4449,15279,48567,158837,532415,1704777,
%T A340410 5547148,18335536,58815602,190574866,623885902,2000945191,6459510350,
%U A340410 20998728429,67275468661,216477522426,699952967976,2239210854373,7184690267832,23131348476391
%N A340410 Number of sets of nonempty words with a total of n letters over ternary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340410 Alois P. Heinz, <a href="/A340410/b340410.txt">Table of n, a(n) for n = 0..1000</a>
%F A340410 G.f.: Product_{j>=1} (1+x^j)^A092255(j).
%e A340410 a(3) = 13: {aaa}, {aab}, {aba}, {baa}, {abc}, {acb}, {bac}, {bca}, {cab}, {cba}, {aa,a}, {ab,a}, {ba,a}.
%p A340410 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340410       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340410     end:
%p A340410 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340410 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340410       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340410     end:
%p A340410 a:= n-> h(n$2, min(n, 3)):
%p A340410 seq(a(n), n=0..32);
%Y A340410 Column k=3 of A292795.
%Y A340410 Cf. A092255.
%K A340410 nonn
%O A340410 0,3
%A A340410 _Alois P. Heinz_, Jan 06 2021