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A272520 Number of set partitions of [n] into eight blocks with distinct sizes. 2
73566121315513295589120000, 302438498741554659644160000, 2585849164240292339957568000, 17681163441201479441398176000, 144230432460463828639480320000, 1126747392322972404668523840000, 11096383744399962905356299840000, 126335461333640259667975104096000 (list; graph; refs; listen; history; text; internal format)
OFFSET

36,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 36..1000

FORMULA

a(n) = n! * [x^n*y^8] Product_{n>=1} (1+y*x^n/n!).

MAPLE

b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n

      or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n, i))))

    end:

a:= n-> b(n$2, 8):

seq(a(n), n=36..45);

CROSSREFS

Column k=8 of A131632.

Sequence in context: A281907 A246288 A246255 * A265913 A217425 A214266

Adjacent sequences:  A272517 A272518 A272519 * A272521 A272522 A272523

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified February 23 06:00 EST 2020. Contains 332159 sequences. (Running on oeis4.)