A306030 - OEIS

%I #5 Jun 17 2018 14:16:52

%S 1,6,57,685,9780,160201,2943277,59687920,1320233315,31557691541,

%T 809161436022,22121068343155,641530646758325,19651776950222806,

%U 633510644286624717,21422880077590022265,757789084383273607060,27969244566731240796621,1074750913823536151018737

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

%H Alois P. Heinz, <a href="/A306030/b306030.txt">Table of n, a(n) for n = 0..431</a>

%F E.g.f.: exp(Sum_{j=1..6} (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+6))

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

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

%Y Column k=6 of A306024.

%Y Cf. A305966.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 17 2018