A306032 Number of length-n restricted growth strings (RGS) with growth <= eight and first element in [8].

1, 8, 100, 1580, 29632, 637220, 15363376, 408744260, 11858631472, 371738275844, 12498545568496, 447999414313412, 17033296095318832, 684009592157461508, 28904630032314771184, 1281216363971401581764, 59402574686629293902896, 2873649326399265142739972

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..413

Crossrefs

Column k=8 of A306024.

Cf. A305968.

Programs

Maple

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

Formula

E.g.f.: exp(Sum_{j=1..8} (exp(j*x)-1)/j).