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A305777 Number of set partitions of [n] with alternating parity of elements and exactly three blocks. 2
1, 3, 7, 14, 30, 57, 119, 224, 460, 867, 1761, 3338, 6734, 12861, 25843, 49748, 99744, 193431, 387365, 756062, 1513138, 2969265, 5940567, 11708072, 23420228, 46317195, 92642569, 183707186, 367430742, 730111269, 1460255291, 2906227196, 5812519912, 11582124159 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (3,4,-18,1,33,-16,-18,12)

FORMULA

G.f.: (10*x^6 -x^5 -13*x^4 +x^3 +6*x^2-1) *x^3 / ((2*x-1) *(x+1) *(3*x^2-1) *(2*x^2-1) *(x-1)^2).

EXAMPLE

a(5) = 7: 123|4|5, 12|34|5, 12|3|45, 1|234|5, 145|2|3, 1|2|345, 1|23|45.

CROSSREFS

Column k=3 of A274581.

Sequence in context: A074988 A265381 A066225 * A139817 A173010 A036892

Adjacent sequences:  A305774 A305775 A305776 * A305778 A305779 A305780

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 10 2018

STATUS

approved

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)