A306033 Number of length-n restricted growth strings (RGS) with growth <= nine and first element in [9].

1, 9, 126, 2229, 46791, 1126032, 30377223, 904211997, 29347973748, 1029154793775, 38706399597879, 1551902279238186, 65998768155695109, 2964410257125490269, 140111251278756345054, 6946234487211269640633, 360202406323880296650987, 19488725004898446787394016

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..406

Crossrefs

Column k=9 of A306024.

Cf. A305969.

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, 0):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..9)), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

E.g.f.: exp(Sum_{j=1..9} (exp(j*x)-1)/j).