A305966 Number of length-n restricted growth strings (RGS) with growth <= six and fixed first element.

1, 1, 7, 70, 875, 12887, 216552, 4065775, 84022595, 1889844292, 45857269017, 1191971998455, 32996489835190, 968034453578997, 29972909437783507, 975944207096597110, 33313664777283768535, 1188852507118147925627, 44246989258071738375272, 1713739685432232160181115

Offset: 0

Author

Alois P. Heinz, Jun 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..432

Crossrefs

Column k=6 of A305962.

Cf. A306030.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+6))
    end:
a:= n-> b(n, -5):
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..6)), x, n), x, n-1)):
seq(a(n), n=0..25);

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..6} (exp(j*x)-1)/j) for n>0, a(0) = 1.