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Number of set partitions of [n] with alternating parity of elements and exactly four blocks.
2

%I #9 Jun 10 2018 13:29:21

%S 1,4,12,33,84,222,545,1425,3458,8948,21595,55335,133144,338530,813249,

%T 2056245,4935870,12432432,29833463,74952867,179842724,451071998,

%U 1082309293,2711584785,6506473162,16289249356,39088013091,97811687679,234720639024,587166227226

%N Number of set partitions of [n] with alternating parity of elements and exactly four blocks.

%H Alois P. Heinz, <a href="/A305778/b305778.txt">Table of n, a(n) for n = 4..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,18,-18,-127,127,450,-450,-844,844,792,-792,-288,288)

%F G.f.: (72*x^11 -84*x^10 -258*x^9 +60*x^8 +287*x^7 +29*x^6 -141*x^5 -34*x^4 +33*x^3 +10*x^2 -3*x-1) *x^4 / ((2*x+1) *(2*x-1) *(x+1) *(6*x^2-1) *(3*x^2-1) *(x-1)^2 *(2*x^2-1)^2).

%e a(5) = 4: 12|3|4|5, 1|23|4|5, 1|2|34|5, 1|2|3|45.

%Y Column k=4 of A274581.

%K nonn,easy

%O 4,2

%A _Alois P. Heinz_, Jun 10 2018