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A305968 Number of length-n restricted growth strings (RGS) with growth <= eight and fixed first element. 3
1, 1, 9, 117, 1905, 36585, 802221, 19664325, 530764089, 15596609985, 494555435781, 16802009359677, 608027982857169, 23322183958778553, 944242763282027421, 40207158379868421429, 1795007963258388557673, 83786699444454149125041, 4079132811705470375924277 (list; graph; refs; listen; history; text; internal format)
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 * A081629 A051617 A166823

Adjacent sequences:  A305965 A305966 A305967 * A305969 A305970 A305971

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2018

STATUS

approved

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Last modified October 21 11:38 EDT 2019. Contains 328296 sequences. (Running on oeis4.)