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A305970 Number of length-n restricted growth strings (RGS) with growth <= ten and fixed first element.

%I A305970 #11 Jun 17 2018 14:49:28
%S A305970 1,1,11,176,3531,83611,2261534,68402389,2278643499,82654180884,
%T A305970 3235722405487,135734461882371,6065518222891786,287319811049356921,
%U A305970 14366920922020964539,755605044476363993912,41667154360185375211619,2402483802700920413411739
%N A305970 Number of length-n restricted growth strings (RGS) with growth <= ten and fixed first element.
%H A305970 Alois P. Heinz, <a href="/A305970/b305970.txt">Table of n, a(n) for n = 0..400</a>
%F A305970 a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..10} (exp(j*x)-1)/j) for n>0, a(0) = 1.
%p A305970 b:= proc(n, m) option remember; `if`(n=0, 1,
%p A305970       add(b(n-1, max(m, j)), j=1..m+10))
%p A305970     end:
%p A305970 a:= n-> b(n, -9):
%p A305970 seq(a(n), n=0..25);
%p A305970 # second Maple program:
%p A305970 a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
%p A305970            (exp(j*x)-1)/j, j=1..10)), x, n), x, n-1)):
%p A305970 seq(a(n), n=0..25);
%Y A305970 Column k=10 of A305962.
%Y A305970 Cf. A306034.
%K A305970 nonn
%O A305970 0,3
%A A305970 _Alois P. Heinz_, Jun 15 2018