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A145458 Exponential transform of C(n,8) = A000581. 2
1, 0, 0, 0, 0, 0, 0, 0, 1, 9, 45, 165, 495, 1287, 3003, 6435, 19305, 243100, 3981978, 49959702, 498967170, 4190469570, 30728937690, 201931408074, 1213163827326, 6849350570700, 39615797628550, 296414654550300, 3418235092302030 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 8 balls are seen at the top.

a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 8 labels.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

E.g.f.: exp(exp(x)*x^8/8!).

MAPLE

a:= proc(n) option remember; `if`(n=0, 1,

      add(binomial(n-1, j-1) *binomial(j, 8) *a(n-j), j=1..n))

    end:

seq(a(n), n=0..35);

CROSSREFS

8th column of A145460, A143398.

Sequence in context: A306939 A229889 A243743 * A145137 A221142 A144902

Adjacent sequences:  A145455 A145456 A145457 * A145459 A145460 A145461

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 10 2008

STATUS

approved

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Last modified December 11 12:33 EST 2019. Contains 329916 sequences. (Running on oeis4.)