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A340413 Number of sets of nonempty words with a total of n letters over senary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340413 #7 Jan 07 2021 17:06:13
%S A340413 1,1,3,13,60,326,2065,9468,51325,268339,1534485,8421447,51259855,
%T A340413 271291165,1568129440,8793678911,51467662027,290934776639,
%U A340413 1758652551885,9783478684069,57676281958781,331610976485751,1959129522047734,11269354282135629,67953764278371963
%N A340413 Number of sets of nonempty words with a total of n letters over senary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340413 Alois P. Heinz, <a href="/A340413/b340413.txt">Table of n, a(n) for n = 0..1000</a>
%F A340413 G.f.: Product_{j>=1} (1+x^j)^A226876(j).
%p A340413 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340413       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340413     end:
%p A340413 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340413 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340413       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340413     end:
%p A340413 a:= n-> h(n$2, min(n, 6)):
%p A340413 seq(a(n), n=0..32);
%Y A340413 Column k=6 of A292795.
%Y A340413 Cf. A226876.
%K A340413 nonn
%O A340413 0,3
%A A340413 _Alois P. Heinz_, Jan 06 2021