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A306031 Number of length-n restricted growth strings (RGS) with growth <= seven and first element in [7].

%I A306031 #5 Jun 17 2018 14:26:35
%S A306031 1,7,77,1071,17689,335083,7117789,166862583,4266097185,117856459427,
%T A306031 3492369757317,110332338885167,3697474419284233,130877053323860507,
%U A306031 4875005854140483629,190478720135836588519,7784916624799021983345,331981949761308979115795
%N A306031 Number of length-n restricted growth strings (RGS) with growth <= seven and first element in [7].
%H A306031 Alois P. Heinz, <a href="/A306031/b306031.txt">Table of n, a(n) for n = 0..421</a>
%F A306031 E.g.f.: exp(Sum_{j=1..7} (exp(j*x)-1)/j).
%p A306031 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A306031       add(b(n-1, max(m, j)), j=1..m+7))
%p A306031     end:
%p A306031 a:= n-> b(n, 0):
%p A306031 seq(a(n), n=0..25);
%p A306031 # second Maple program:
%p A306031 a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..7)), x, n+1), x, n):
%p A306031 seq(a(n), n=0..25);
%Y A306031 Column k=7 of A306024.
%Y A306031 Cf. A305967.
%K A306031 nonn
%O A306031 0,2
%A A306031 _Alois P. Heinz_, Jun 17 2018