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A305968 Number of length-n restricted growth strings (RGS) with growth <= eight and fixed first element.

%I A305968 #11 Jun 17 2018 14:30:32
%S A305968 1,1,9,117,1905,36585,802221,19664325,530764089,15596609985,
%T A305968 494555435781,16802009359677,608027982857169,23322183958778553,
%U A305968 944242763282027421,40207158379868421429,1795007963258388557673,83786699444454149125041,4079132811705470375924277
%N A305968 Number of length-n restricted growth strings (RGS) with growth <= eight and fixed first element.
%H A305968 Alois P. Heinz, <a href="/A305968/b305968.txt">Table of n, a(n) for n = 0..414</a>
%F A305968 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..8} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305968 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305968       add(b(n-1, max(m, j)), j=1..m+8))
%p A305968     end:
%p A305968 a:= n-> b(n, -7):
%p A305968 seq(a(n), n=0..25);
%p A305968 # second Maple program:
%p A305968 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305968            (exp(j*x)-1)/j, j=1..8)), x, n), x, n-1)):
%p A305968 seq(a(n), n=0..25);
%Y A305968 Column k=8 of A305962.
%Y A305968 Cf. A306032.
%K A305968 nonn
%O A305968 0,3
%A A305968 _Alois P. Heinz_, Jun 15 2018