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A306029 Number of length-n restricted growth strings (RGS) with growth <= five and first element in [5].

%I A306029 #6 Jun 17 2018 14:20:18
%S A306029 1,5,40,405,4875,67354,1044045,17867125,333554020,6730070329,
%T A306029 145676361731,3362266525430,82326965117385,2129349953723509,
%U A306029 57961263778376192,1655067729384150829,49437118345913831595,1540860755766376984434,50000885646431513577973
%N A306029 Number of length-n restricted growth strings (RGS) with growth <= five and first element in [5].
%H A306029 Alois P. Heinz, <a href="/A306029/b306029.txt">Table of n, a(n) for n = 0..444</a>
%F A306029 E.g.f.: exp(Sum_{j=1..5} (exp(j*x)-1)/j).
%p A306029 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306029       add(b(n-1, max(m, j)), j=1..m+5))
%p A306029     end:
%p A306029 a:= n-> b(n, 0):
%p A306029 seq(a(n), n=0..25);
%p A306029 # second Maple program:
%p A306029 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..5)), x, n+1), x, n):
%p A306029 seq(a(n), n=0..25);
%Y A306029 Column k=5 of A306024.
%Y A306029 Cf. A305965.
%K A306029 nonn
%O A306029 0,2
%A A306029 _Alois P. Heinz_, Jun 17 2018