A305778 Number of set partitions of [n] with alternating parity of elements and exactly four blocks.

1, 4, 12, 33, 84, 222, 545, 1425, 3458, 8948, 21595, 55335, 133144, 338530, 813249, 2056245, 4935870, 12432432, 29833463, 74952867, 179842724, 451071998, 1082309293, 2711584785, 6506473162, 16289249356, 39088013091, 97811687679, 234720639024, 587166227226

Offset: 4

Author

Alois P. Heinz, Jun 10 2018

Keywords

• nonn
• easy

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (1,18,-18,-127,127,450,-450,-844,844,792,-792,-288,288)

Crossrefs

Column k=4 of A274581.

Formula

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).