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A305965 Number of length-n restricted growth strings (RGS) with growth <= five and fixed first element.

%I A305965 #14 Jun 17 2018 14:19:54
%S A305965 1,1,6,51,541,6756,96205,1530025,26775550,509861195,10472109149,
%T A305965 230368347780,5396308081285,133949699318945,3508794554854054,
%U A305965 96648143868171171,2790590111082279405,84231759174460743700,2651416546964399982909,86848041397350751409257
%N A305965 Number of length-n restricted growth strings (RGS) with growth <= five and fixed first element.
%H A305965 Alois P. Heinz, <a href="/A305965/b305965.txt">Table of n, a(n) for n = 0..444</a>
%F A305965 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..5} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305965 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305965       add(b(n-1, max(m, j)), j=1..m+5))
%p A305965     end:
%p A305965 a:= n-> b(n, -4):
%p A305965 seq(a(n), n=0..25);
%p A305965 # second Maple program:
%p A305965 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305965            (exp(j*x)-1)/j, j=1..5)), x, n), x, n-1)):
%p A305965 seq(a(n), n=0..25);
%Y A305965 Column k=5 of A305962.
%Y A305965 Cf. A306029.
%K A305965 nonn
%O A305965 0,3
%A A305965 _Alois P. Heinz_, Jun 15 2018