cp's OEIS Frontend

A340414 Number of sets of nonempty words with a total of n letters over septenary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A340414 #6 Jan 06 2021 20:43:23
%S A340414 1,1,3,13,60,326,2065,14508,76525,454819,2718885,16777767,107808655,
%T A340414 697287805,4748992600,29397584111,190989109387,1239766891439,
%U A340414 8159345112885,54161955000133,360150593097845,2454684519628143,16056425089104526,107300319826659573
%N A340414 Number of sets of nonempty words with a total of n letters over septenary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A340414 Alois P. Heinz, <a href="/A340414/b340414.txt">Table of n, a(n) for n = 0..1000</a>
%F A340414 G.f.: Product_{j>=1} (1+x^j)^A226877(j).
%p A340414 b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
%p A340414       add(b(n-j, j, t-1)/j!, j=i..n/t))
%p A340414     end:
%p A340414 g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
%p A340414 h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A340414       add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
%p A340414     end:
%p A340414 a:= n-> h(n$2, min(n, 7)):
%p A340414 seq(a(n), n=0..32);
%Y A340414 Column k=7 of A292795.
%Y A340414 Cf. A226877.
%K A340414 nonn
%O A340414 0,3
%A A340414 _Alois P. Heinz_, Jan 06 2021