cp's OEIS Frontend

A305964 Number of length-n restricted growth strings (RGS) with growth <= four and fixed first element.

%I A305964 #13 Jun 17 2018 14:04:30
%S A305964 1,1,5,35,305,3125,36479,475295,6811205,106170245,1784531879,
%T A305964 32117927231,615413731205,12493421510405,267608512061159,
%U A305964 6026688403933967,142256385130774229,3509899012049396645,90301862963332188839,2417349828110572405823,67201548131159391828677
%N A305964 Number of length-n restricted growth strings (RGS) with growth <= four and fixed first element.
%H A305964 Alois P. Heinz, <a href="/A305964/b305964.txt">Table of n, a(n) for n = 0..460</a>
%F A305964 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..4} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305964 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305964       add(b(n-1, max(m, j)), j=1..m+4))
%p A305964     end:
%p A305964 a:= n-> b(n, -3):
%p A305964 seq(a(n), n=0..25);
%p A305964 # second Maple program:
%p A305964 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305964            (exp(j*x)-1)/j, j=1..4)), x, n), x, n-1)):
%p A305964 seq(a(n), n=0..25);
%Y A305964 Column k=4 of A305962.
%Y A305964 Cf. A306028.
%K A305964 nonn
%O A305964 0,3
%A A305964 _Alois P. Heinz_, Jun 15 2018