A305968 Number of length-n restricted growth strings (RGS) with growth <= eight and fixed first element.

1, 1, 9, 117, 1905, 36585, 802221, 19664325, 530764089, 15596609985, 494555435781, 16802009359677, 608027982857169, 23322183958778553, 944242763282027421, 40207158379868421429, 1795007963258388557673, 83786699444454149125041, 4079132811705470375924277

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..414

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..8} (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+8))
    end:
a:= n-> b(n, -7):
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..8)), x, n), x, n-1)):
seq(a(n), n=0..25);

Crossrefs

Column k=8 of A305962.

Cf. A306032.

Sequence in context: A027396 A294190 A113344 * A367473 A081629 A051617

Adjacent sequences: A305965 A305966 A305967 * A305969 A305970 A305971

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved