cp's OEIS Frontend

A340411 Number of sets of nonempty words with a total of n letters over quaternary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340411 #5 Jan 06 2021 19:58:39
%S A340411 1,1,3,13,60,206,865,3408,15025,57175,240741,961035,4132903,16279273,
%T A340411 68134510,274714351,1164578487,4657730815,19404869767,78676610521,
%U A340411 330495175277,1332463920931,5531856232294,22498784991153,93925698566719,380437352382876
%N A340411 Number of sets of nonempty words with a total of n letters over quaternary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340411 Alois P. Heinz, <a href="/A340411/b340411.txt">Table of n, a(n) for n = 0..1000</a>
%F A340411 G.f.: Product_{j>=1} (1+x^j)^A092429(j).
%p A340411 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340411       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340411     end:
%p A340411 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340411 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340411       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340411     end:
%p A340411 a:= n-> h(n$2, min(n, 4)):
%p A340411 seq(a(n), n=0..32);
%Y A340411 Column k=4 of A292795.
%Y A340411 Cf. A092429.
%K A340411 nonn
%O A340411 0,3
%A A340411 _Alois P. Heinz_, Jan 06 2021