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A272518 Number of set partitions of [n] into six blocks with distinct sizes. 2
2053230379200, 6453009763200, 43288940494800, 242418066770880, 1707999012720000, 12887361202716000, 144924867388501200, 620550897351184800, 4048435123506774000, 23424084614648718000, 161250104584826056800, 1013722794731975328000, 8616255173755280251200 (list; graph; refs; listen; history; text; internal format)
OFFSET

21,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 21..1000

FORMULA

a(n) = n! * [x^n*y^6] 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, 6):

seq(a(n), n=21..40);

CROSSREFS

Column k=6 of A131632.

Sequence in context: A233601 A233850 A274808 * A246233 A234053 A032756

Adjacent sequences:  A272515 A272516 A272517 * A272519 A272520 A272521

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)