cp's OEIS Frontend

A293737 Number of multisets of nonempty words with a total of n letters over septenary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A293737 #9 May 30 2019 09:27:55
%S A293737 1,1,3,7,20,54,164,500,1629,5462,19164,69457,261154,1012164,4045640,
%T A293737 16611121,70001515,301922104,1331128134,5986321599,27426419974,
%U A293737 127801386949,605016657100,2906093083727,14149469612919,69762426194708,348016146152252,1755188873640756
%N A293737 Number of multisets of nonempty words with a total of n letters over septenary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%C A293737 This sequence differs from A293110 first at n=8.
%H A293737 Alois P. Heinz, <a href="/A293737/b293737.txt">Table of n, a(n) for n = 0..1000</a>
%F A293737 G.f.: Product_{j>=1} 1/(1-x^j)^A007578(j).
%F A293737 a(n) ~ c * 7^n / n^(21/2), where c = 233774941.39802934196800791705821024006230754487492494942398064537776753785... - _Vaclav Kotesovec_, May 30 2019
%p A293737 g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
%p A293737       ((4*n^3+78*n^2+424*n+495)*g(n-1) +(n-1)*(34*n^2+280*n+
%p A293737        305)*g(n-2) -2*(n-1)*(n-2)*(38*n+145)*g(n-3) -105*(n-1)
%p A293737        *(n-2)*(n-3)*g(n-4))/((n+6)*(n+10)*(n+12)))
%p A293737     end:
%p A293737 a:= proc(n) option remember; `if`(n=0, 1, add(add(g(d)
%p A293737       *d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p A293737     end:
%p A293737 seq(a(n), n=0..35);
%Y A293737 Column k=7 of A293108.
%Y A293737 Cf. A007578, A293110, A293746.
%K A293737 nonn
%O A293737 0,3
%A A293737 _Alois P. Heinz_, Oct 15 2017