A305969 Number of length-n restricted growth strings (RGS) with growth <= nine and fixed first element.

1, 1, 10, 145, 2635, 56500, 1383583, 37881805, 1142217640, 37498693555, 1328537843683, 50433784870174, 2039431564419565, 87417904301582485, 3955287872973269098, 188224672012964294293, 9391435700578827609247, 489942796606580418069220, 26659613135178842578434283

Offset: 0

Author

Alois P. Heinz, Jun 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..407

Crossrefs

Column k=9 of A305962.

Cf. A306033.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+9))
    end:
a:= n-> b(n, -8):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
           (exp(j*x)-1)/j, j=1..9)), x, n), x, n-1)):
seq(a(n), n=0..25);

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..9} (exp(j*x)-1)/j) for n>0, a(0) = 1.