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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
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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:
A338957
A338953
A345296
*
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 May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)