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Number of length-n restricted growth strings (RGS) with growth <= ten and fixed first element.
3

%I #11 Jun 17 2018 14:49:28

%S 1,1,11,176,3531,83611,2261534,68402389,2278643499,82654180884,

%T 3235722405487,135734461882371,6065518222891786,287319811049356921,

%U 14366920922020964539,755605044476363993912,41667154360185375211619,2402483802700920413411739

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

%H Alois P. Heinz, <a href="/A305970/b305970.txt">Table of n, a(n) for n = 0..400</a>

%F 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 b:= proc(n, m) option remember; `if`(n=0, 1,

%p add(b(n-1, max(m, j)), j=1..m+10))

%p end:

%p a:= n-> b(n, -9):

%p seq(a(n), n=0..25);

%p # second Maple program:

%p a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(

%p (exp(j*x)-1)/j, j=1..10)), x, n), x, n-1)):

%p seq(a(n), n=0..25);

%Y Column k=10 of A305962.

%Y Cf. A306034.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 15 2018