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A275283 Number of set partitions of [2n] with symmetric block size list of length n. 4
1, 1, 3, 19, 171, 2066, 31346, 559987, 11954993, 282835456, 7785919355, 229359684137, 7731656573016, 272633076900991, 10876116332074739, 446659746000614675, 20580725671071449149, 964732749192326683508, 50418595763262446272127, 2656265906893413392905767 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

Wikipedia, Partition of a set

FORMULA

a(n) = A275281(2n,n).

a(n) ~ c * n^(n-1/2) * d^n / (exp(n) * 2^(n-3/2)), where d = 5.99720652866734051428..., c = 0.331364442872654716... if n is even and c = 0.32118925729236323... if n is odd. - Vaclav Kotesovec, Aug 08 2016

EXAMPLE

a(0) = 1: {}.

a(1) = 1: 12.

a(2) = 3: 12|34, 13|24, 14|23.

a(3) = 19: 12|34|56, 12|35|46, 12|36|45, 13|24|56, 13|25|46, 13|26|45, 14|23|56, 1|2345|6, 1|2346|5, 15|23|46, 1|2356|4, 16|23|45, 14|25|36, 14|26|35, 15|24|36, 1|2456|3, 16|24|35, 15|26|34, 16|25|34.

CROSSREFS

Bisection (even part) of A305197.

Cf. A275281.

Sequence in context: A080894 A143768 A256493 * A083071 A305459 A045531

Adjacent sequences:  A275280 A275281 A275282 * A275284 A275285 A275286

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 21 2016

STATUS

approved

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Last modified February 23 00:18 EST 2019. Contains 320411 sequences. (Running on oeis4.)