A305964 - OEIS

%I #13 Jun 17 2018 14:04:30

%S 1,1,5,35,305,3125,36479,475295,6811205,106170245,1784531879,

%T 32117927231,615413731205,12493421510405,267608512061159,

%U 6026688403933967,142256385130774229,3509899012049396645,90301862963332188839,2417349828110572405823,67201548131159391828677

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

%H Alois P. Heinz, <a href="/A305964/b305964.txt">Table of n, a(n) for n = 0..460</a>

%F 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 b:= proc(n, m) option remember; `if`(n=0, 1,

%p       add(b(n-1, max(m, j)), j=1..m+4))

%p     end:

%p a:= n-> b(n, -3):

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

%p # second Maple program:

%p a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(

%p            (exp(j*x)-1)/j, j=1..4)), x, n), x, n-1)):

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

%Y Column k=4 of A305962.

%Y Cf. A306028.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 15 2018