A305967 Number of length-n restricted growth strings (RGS) with growth <= seven and fixed first element.

1, 1, 8, 92, 1324, 22464, 435044, 9416240, 224382116, 5820361008, 162900823428, 4884515258224, 155992931417316, 5280138035455024, 188639017788288836, 7087660960768335472, 279189959071013966500, 11498108706476961892400, 493881446025566760548100

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..422

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..7} (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+7))
    end:
a:= n-> b(n, -6):
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..7)), x, n), x, n-1)):
seq(a(n), n=0..25);

Crossrefs

Column k=7 of A305962.

Cf. A306031.

Sequence in context: A027395 A277307 A255520 * A113353 A081624 A298188

Adjacent sequences: A305964 A305965 A305966 * A305968 A305969 A305970

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved