cp's OEIS Frontend

A305966 Number of length-n restricted growth strings (RGS) with growth <= six and fixed first element.

%I A305966 #11 Jun 17 2018 14:16:37
%S A305966 1,1,7,70,875,12887,216552,4065775,84022595,1889844292,45857269017,
%T A305966 1191971998455,32996489835190,968034453578997,29972909437783507,
%U A305966 975944207096597110,33313664777283768535,1188852507118147925627,44246989258071738375272,1713739685432232160181115
%N A305966 Number of length-n restricted growth strings (RGS) with growth <= six and fixed first element.
%H A305966 Alois P. Heinz, <a href="/A305966/b305966.txt">Table of n, a(n) for n = 0..432</a>
%F A305966 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..6} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305966 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305966       add(b(n-1, max(m, j)), j=1..m+6))
%p A305966     end:
%p A305966 a:= n-> b(n, -5):
%p A305966 seq(a(n), n=0..25);
%p A305966 # second Maple program:
%p A305966 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305966            (exp(j*x)-1)/j, j=1..6)), x, n), x, n-1)):
%p A305966 seq(a(n), n=0..25);
%Y A305966 Column k=6 of A305962.
%Y A305966 Cf. A306030.
%K A305966 nonn
%O A305966 0,3
%A A305966 _Alois P. Heinz_, Jun 15 2018