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A306032 Number of length-n restricted growth strings (RGS) with growth <= eight and first element in [8].

%I A306032 #5 Jun 17 2018 14:30:57
%S A306032 1,8,100,1580,29632,637220,15363376,408744260,11858631472,
%T A306032 371738275844,12498545568496,447999414313412,17033296095318832,
%U A306032 684009592157461508,28904630032314771184,1281216363971401581764,59402574686629293902896,2873649326399265142739972
%N A306032 Number of length-n restricted growth strings (RGS) with growth <= eight and first element in [8].
%H A306032 Alois P. Heinz, <a href="/A306032/b306032.txt">Table of n, a(n) for n = 0..413</a>
%F A306032 E.g.f.: exp(Sum_{j=1..8} (exp(j*x)-1)/j).
%p A306032 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306032       add(b(n-1, max(m, j)), j=1..m+8))
%p A306032     end:
%p A306032 a:= n-> b(n, 0):
%p A306032 seq(a(n), n=0..25);
%p A306032 # second Maple program:
%p A306032 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..8)), x, n+1), x, n):
%p A306032 seq(a(n), n=0..25);
%Y A306032 Column k=8 of A306024.
%Y A306032 Cf. A305968.
%K A306032 nonn
%O A306032 0,2
%A A306032 _Alois P. Heinz_, Jun 17 2018