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A306034 Number of length-n restricted growth strings (RGS) with growth <= ten and first element in [10].

%I A306034 #5 Jun 17 2018 14:49:51
%S A306034 1,10,155,3035,70500,1877083,56019305,1844512570,66219313755,
%T A306034 2568394851483,106837050484924,4737487302902715,222819378516865825,
%U A306034 11068264704881204698,578536038611685742843,31718762374848254987147,1818933941414434687198820
%N A306034 Number of length-n restricted growth strings (RGS) with growth <= ten and first element in [10].
%H A306034 Alois P. Heinz, <a href="/A306034/b306034.txt">Table of n, a(n) for n = 0..400</a>
%F A306034 E.g.f.: exp(Sum_{j=1..10} (exp(j*x)-1)/j).
%p A306034 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306034       add(b(n-1, max(m, j)), j=1..m+10))
%p A306034     end:
%p A306034 a:= n-> b(n, 0):
%p A306034 seq(a(n), n=0..25);
%p A306034 # second Maple program:
%p A306034 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..10)), x, n+1), x, n):
%p A306034 seq(a(n), n=0..25);
%Y A306034 Column k=10 of A306024.
%Y A306034 Cf. A305970.
%K A306034 nonn
%O A306034 0,2
%A A306034 _Alois P. Heinz_, Jun 17 2018