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A327885 Number of set partitions of [n] such that at least one of the block sizes is 2. 3
0, 0, 1, 3, 9, 35, 150, 672, 3269, 17271, 97155, 578985, 3654750, 24331320, 170074177, 1244911605, 9520843575, 75890001665, 629104453236, 5413637745144, 48277814341765, 445463898405225, 4246785220234557, 41775507558584283, 423516880995944532 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

FORMULA

E.g.f.: exp(exp(x)-1) - exp(exp(x)-1-x^2/2).

a(n) = A000110(n) - A097514(n).

EXAMPLE

a(2) = 1: 12.

a(3) = 3: 12|3, 13|2, 1|23.

a(4) = 9: 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|24|3, 1|2|34.

a(5) = 35: 123|45, 124|35, 125|34, 12|345, 12|34|5, 12|35|4, 12|3|45, 12|3|4|5, 134|25, 135|24, 13|245, 13|24|5, 13|25|4, 13|2|45, 13|2|4|5, 145|23, 14|235, 14|23|5, 15|234, 15|23|4, 1|23|45, 1|23|4|5, 14|25|3, 14|2|35, 14|2|3|5, 15|24|3, 1|24|35, 1|24|3|5, 15|2|34, 1|25|34, 1|2|34|5, 15|2|3|4, 1|25|3|4, 1|2|35|4, 1|2|3|45.

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1, add(

      `if`(j=k, 0, b(n-j, k)*binomial(n-1, j-1)), j=1..n))

    end:

a:= n-> b(n, 0)-b(n, 2):

seq(a(n), n=0..27);

CROSSREFS

Column k=2 of A327884.

Cf. A000110, A097514.

Sequence in context: A046697 A151045 A225041 * A074507 A217924 A030268

Adjacent sequences:  A327881 A327882 A327884 * A327887 A327889 A327890

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 28 2019

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)