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A305969 Number of length-n restricted growth strings (RGS) with growth <= nine and fixed first element. 3
1, 1, 10, 145, 2635, 56500, 1383583, 37881805, 1142217640, 37498693555, 1328537843683, 50433784870174, 2039431564419565, 87417904301582485, 3955287872973269098, 188224672012964294293, 9391435700578827609247, 489942796606580418069220, 26659613135178842578434283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..407

FORMULA

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..9} (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+9))

    end:

a:= n-> b(n, -8):

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..9)), x, n), x, n-1)):

seq(a(n), n=0..25);

CROSSREFS

Column k=9 of A305962.

Cf. A306033.

Sequence in context: A255522 A113354 A027397 * A081697 A134526 A297714

Adjacent sequences:  A305966 A305967 A305968 * A305970 A305971 A305972

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2018

STATUS

approved

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Last modified September 22 02:31 EDT 2021. Contains 347605 sequences. (Running on oeis4.)