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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
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 15 2018
STATUS
approved