A305968 - OEIS

%I #11 Jun 17 2018 14:30:32

%S 1,1,9,117,1905,36585,802221,19664325,530764089,15596609985,

%T 494555435781,16802009359677,608027982857169,23322183958778553,

%U 944242763282027421,40207158379868421429,1795007963258388557673,83786699444454149125041,4079132811705470375924277

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

%H Alois P. Heinz, <a href="/A305968/b305968.txt">Table of n, a(n) for n = 0..414</a>

%F a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..8} (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+8))

%p     end:

%p a:= n-> b(n, -7):

%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..8)), x, n), x, n-1)):

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

%Y Column k=8 of A305962.

%Y Cf. A306032.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 15 2018