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