A305967 Number of length-n restricted growth strings (RGS) with growth <= seven and fixed first element.

1, 1, 8, 92, 1324, 22464, 435044, 9416240, 224382116, 5820361008, 162900823428, 4884515258224, 155992931417316, 5280138035455024, 188639017788288836, 7087660960768335472, 279189959071013966500, 11498108706476961892400, 493881446025566760548100

Offset: 0

Author

Alois P. Heinz, Jun 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..422

Crossrefs

Column k=7 of A305962.

Cf. A306031.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+7))
    end:
a:= n-> b(n, -6):
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..7)), x, n), x, n-1)):
seq(a(n), n=0..25);

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..7} (exp(j*x)-1)/j) for n>0, a(0) = 1.