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A305969 Number of length-n restricted growth strings (RGS) with growth <= nine and fixed first element.

%I A305969 #11 Jun 17 2018 14:45:18
%S A305969 1,1,10,145,2635,56500,1383583,37881805,1142217640,37498693555,
%T A305969 1328537843683,50433784870174,2039431564419565,87417904301582485,
%U A305969 3955287872973269098,188224672012964294293,9391435700578827609247,489942796606580418069220,26659613135178842578434283
%N A305969 Number of length-n restricted growth strings (RGS) with growth <= nine and fixed first element.
%H A305969 Alois P. Heinz, <a href="/A305969/b305969.txt">Table of n, a(n) for n = 0..407</a>
%F A305969 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..9} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305969 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305969       add(b(n-1, max(m, j)), j=1..m+9))
%p A305969     end:
%p A305969 a:= n-> b(n, -8):
%p A305969 seq(a(n), n=0..25);
%p A305969 # second Maple program:
%p A305969 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305969            (exp(j*x)-1)/j, j=1..9)), x, n), x, n-1)):
%p A305969 seq(a(n), n=0..25);
%Y A305969 Column k=9 of A305962.
%Y A305969 Cf. A306033.
%K A305969 nonn
%O A305969 0,3
%A A305969 _Alois P. Heinz_, Jun 15 2018