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A306033 Number of length-n restricted growth strings (RGS) with growth <= nine and first element in [9].

%I A306033 #5 Jun 17 2018 14:45:42
%S A306033 1,9,126,2229,46791,1126032,30377223,904211997,29347973748,
%T A306033 1029154793775,38706399597879,1551902279238186,65998768155695109,
%U A306033 2964410257125490269,140111251278756345054,6946234487211269640633,360202406323880296650987,19488725004898446787394016
%N A306033 Number of length-n restricted growth strings (RGS) with growth <= nine and first element in [9].
%H A306033 Alois P. Heinz, <a href="/A306033/b306033.txt">Table of n, a(n) for n = 0..406</a>
%F A306033 E.g.f.: exp(Sum_{j=1..9} (exp(j*x)-1)/j).
%p A306033 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306033       add(b(n-1, max(m, j)), j=1..m+9))
%p A306033     end:
%p A306033 a:= n-> b(n, 0):
%p A306033 seq(a(n), n=0..25);
%p A306033 # second Maple program:
%p A306033 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..9)), x, n+1), x, n):
%p A306033 seq(a(n), n=0..25);
%Y A306033 Column k=9 of A306024.
%Y A306033 Cf. A305969.
%K A306033 nonn
%O A306033 0,2
%A A306033 _Alois P. Heinz_, Jun 17 2018