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A327881 Number of set partitions of [n] with distinct block sizes and one of the block sizes is 2. 2
0, 0, 1, 3, 0, 10, 75, 126, 196, 1548, 15525, 39820, 161106, 358722, 3705884, 46623045, 142988280, 768721504, 3560215293, 12250746432, 144581799790, 2542575063630, 8955836934660, 55657973021431, 319349051391228, 1983548989621200, 7898257536096850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Sum of multinomials M(n; lambda), where lambda ranges over all integer partitions of n into distinct parts and one part is 2.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..697

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

Wikipedia, Partition of a set

EXAMPLE

a(2) = 1: 12.

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

a(4) = 0.

a(5) = 10: 123|45, 124|35, 125|34, 12|345, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234.

MAPLE

b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,

     `if`(n=0, 1, `if`(i<2, 0, b(n, i-1, `if`(i=k, 0, k)))+

     `if`(i=k, 0, b(n-i, min(n-i, i-1), k)*binomial(n, i))))

    end:

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

seq(a(n), n=0..29);

CROSSREFS

Column k=2 of A327869.

Sequence in context: A090460 A071983 A302693 * A215514 A215347 A186247

Adjacent sequences:  A327878 A327879 A327880 * A327882 A327883 A327884

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 28 2019

STATUS

approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)