A306032 - OEIS

%I #5 Jun 17 2018 14:30:57

%S 1,8,100,1580,29632,637220,15363376,408744260,11858631472,

%T 371738275844,12498545568496,447999414313412,17033296095318832,

%U 684009592157461508,28904630032314771184,1281216363971401581764,59402574686629293902896,2873649326399265142739972

%N Number of length-n restricted growth strings (RGS) with growth <= eight and first element in [8].

%H Alois P. Heinz, <a href="/A306032/b306032.txt">Table of n, a(n) for n = 0..413</a>

%F E.g.f.: exp(Sum_{j=1..8} (exp(j*x)-1)/j).

%p b:= proc(n, m) option remember; `if`(n=0, 1,

%p       add(b(n-1, max(m, j)), j=1..m+8))

%p     end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=0..25);

%p # second Maple program:

%p a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..8)), x, n+1), x, n):

%p seq(a(n), n=0..25);

%Y Column k=8 of A306024.

%Y Cf. A305968.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 17 2018