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

0,3

Links

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

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.

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);

Crossrefs

Column k=6 of A305962.

Cf. A306030.

Sequence in context: A346767 A209327 A255519 * A226805 A113343 A124566

Adjacent sequences: A305963 A305964 A305965 * A305967 A305968 A305969

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved