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A306028 Number of length-n restricted growth strings (RGS) with growth <= four and first element in [4].

%I A306028 #9 Jun 17 2018 14:05:47
%S A306028 1,4,26,214,2096,23578,297692,4150798,63148652,1038505282,18324165284,
%T A306028 344791676446,6883214479964,145160792680210,3221934217192772,
%U A306028 75022325591768782,1827426669105650588,46448931646662304066,1229212096172351894852,33800410177112965182910
%N A306028 Number of length-n restricted growth strings (RGS) with growth <= four and first element in [4].
%H A306028 Alois P. Heinz, <a href="/A306028/b306028.txt">Table of n, a(n) for n = 0..459</a>
%F A306028 E.g.f.: exp(Sum_{j=1..4} (exp(j*x)-1)/j).
%p A306028 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306028       add(b(n-1, max(m, j)), j=1..m+4))
%p A306028     end:
%p A306028 a:= n-> b(n, 0):
%p A306028 seq(a(n), n=0..25);
%p A306028 # second Maple program:
%p A306028 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..4)), x, n+1), x, n):
%p A306028 seq(a(n), n=0..25);
%Y A306028 Column k=4 of A306024.
%Y A306028 Cf. A305964.
%K A306028 nonn
%O A306028 0,2
%A A306028 _Alois P. Heinz_, Jun 17 2018