cp's OEIS Frontend

A306030 Number of length-n restricted growth strings (RGS) with growth <= six and first element in [6].

%I A306030 #5 Jun 17 2018 14:16:52
%S A306030 1,6,57,685,9780,160201,2943277,59687920,1320233315,31557691541,
%T A306030 809161436022,22121068343155,641530646758325,19651776950222806,
%U A306030 633510644286624717,21422880077590022265,757789084383273607060,27969244566731240796621,1074750913823536151018737
%N A306030 Number of length-n restricted growth strings (RGS) with growth <= six and first element in [6].
%H A306030 Alois P. Heinz, <a href="/A306030/b306030.txt">Table of n, a(n) for n = 0..431</a>
%F A306030 E.g.f.: exp(Sum_{j=1..6} (exp(j*x)-1)/j).
%p A306030 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306030       add(b(n-1, max(m, j)), j=1..m+6))
%p A306030     end:
%p A306030 a:= n-> b(n, 0):
%p A306030 seq(a(n), n=0..25);
%p A306030 # second Maple program:
%p A306030 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..6)), x, n+1), x, n):
%p A306030 seq(a(n), n=0..25);
%Y A306030 Column k=6 of A306024.
%Y A306030 Cf. A305966.
%K A306030 nonn
%O A306030 0,2
%A A306030 _Alois P. Heinz_, Jun 17 2018