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

0,3

Links

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

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.

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);

Crossrefs

Column k=9 of A305962.

Cf. A306033.

Sequence in context: A255522 A113354 A027397 * A081697 A134526 A297714

Adjacent sequences: A305966 A305967 A305968 * A305970 A305971 A305972

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved