A306029 - OEIS

%I #6 Jun 17 2018 14:20:18

%S 1,5,40,405,4875,67354,1044045,17867125,333554020,6730070329,

%T 145676361731,3362266525430,82326965117385,2129349953723509,

%U 57961263778376192,1655067729384150829,49437118345913831595,1540860755766376984434,50000885646431513577973

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

%H Alois P. Heinz, <a href="/A306029/b306029.txt">Table of n, a(n) for n = 0..444</a>

%F E.g.f.: exp(Sum_{j=1..5} (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+5))

%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..5)), x, n+1), x, n):

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

%Y Column k=5 of A306024.

%Y Cf. A305965.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 17 2018