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A305967 Number of length-n restricted growth strings (RGS) with growth <= seven and fixed first element.

%I A305967 #11 Jun 17 2018 14:26:06
%S A305967 1,1,8,92,1324,22464,435044,9416240,224382116,5820361008,162900823428,
%T A305967 4884515258224,155992931417316,5280138035455024,188639017788288836,
%U A305967 7087660960768335472,279189959071013966500,11498108706476961892400,493881446025566760548100
%N A305967 Number of length-n restricted growth strings (RGS) with growth <= seven and fixed first element.
%H A305967 Alois P. Heinz, <a href="/A305967/b305967.txt">Table of n, a(n) for n = 0..422</a>
%F A305967 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..7} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305967 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305967       add(b(n-1, max(m, j)), j=1..m+7))
%p A305967     end:
%p A305967 a:= n-> b(n, -6):
%p A305967 seq(a(n), n=0..25);
%p A305967 # second Maple program:
%p A305967 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305967            (exp(j*x)-1)/j, j=1..7)), x, n), x, n-1)):
%p A305967 seq(a(n), n=0..25);
%Y A305967 Column k=7 of A305962.
%Y A305967 Cf. A306031.
%K A305967 nonn
%O A305967 0,3
%A A305967 _Alois P. Heinz_, Jun 15 2018