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A305777 Number of set partitions of [n] with alternating parity of elements and exactly three blocks.

%I A305777 #10 Jun 10 2018 13:28:58
%S A305777 1,3,7,14,30,57,119,224,460,867,1761,3338,6734,12861,25843,49748,
%T A305777 99744,193431,387365,756062,1513138,2969265,5940567,11708072,23420228,
%U A305777 46317195,92642569,183707186,367430742,730111269,1460255291,2906227196,5812519912,11582124159
%N A305777 Number of set partitions of [n] with alternating parity of elements and exactly three blocks.
%H A305777 Alois P. Heinz, <a href="/A305777/b305777.txt">Table of n, a(n) for n = 3..1000</a>
%H A305777 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%H A305777 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,4,-18,1,33,-16,-18,12)
%F A305777 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).
%e A305777 a(5) = 7: 123|4|5, 12|34|5, 12|3|45, 1|234|5, 145|2|3, 1|2|345, 1|23|45.
%Y A305777 Column k=3 of A274581.
%K A305777 nonn,easy
%O A305777 3,2
%A A305777 _Alois P. Heinz_, Jun 10 2018