A306034 Number of length-n restricted growth strings (RGS) with growth <= ten and first element in [10].

1, 10, 155, 3035, 70500, 1877083, 56019305, 1844512570, 66219313755, 2568394851483, 106837050484924, 4737487302902715, 222819378516865825, 11068264704881204698, 578536038611685742843, 31718762374848254987147, 1818933941414434687198820

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Column k=10 of A306024.

Cf. A305970.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+10))
    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..10)), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

E.g.f.: exp(Sum_{j=1..10} (exp(j*x)-1)/j).