A306029 Number of length-n restricted growth strings (RGS) with growth <= five and first element in [5].

1, 5, 40, 405, 4875, 67354, 1044045, 17867125, 333554020, 6730070329, 145676361731, 3362266525430, 82326965117385, 2129349953723509, 57961263778376192, 1655067729384150829, 49437118345913831595, 1540860755766376984434, 50000885646431513577973

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..444

Crossrefs

Column k=5 of A306024.

Cf. A305965.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+5))
    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..5)), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

E.g.f.: exp(Sum_{j=1..5} (exp(j*x)-1)/j).