A274872 Number of set partitions of [n] into exactly eight blocks such that all odd elements are in blocks with an odd index and all even elements are in blocks with an even index.

1, 4, 50, 200, 1519, 6076, 36564, 146256, 770481, 3081924, 14934774, 59739096, 273905827, 1095623308, 4836291512, 19345166048, 83144608885, 332578435540, 1402399388442, 5609597553768, 23330003686119, 93320014744476, 384220628807964, 1536882515231856

Offset: 8

Author

Alois P. Heinz, Jul 09 2016

Keywords

• nonn
• easy

Examples

			a(8) = 1: 1|2|3|4|5|6|7|8.
a(9) = 4: 19|2|3|4|5|6|7|8, 1|2|39|4|5|6|7|8, 1|2|3|4|59|6|7|8, 1|2|3|4|5|6|79|8.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 of A274537.

Formula

G.f.: -x^8/((x-1)*(3*x-1)*(2*x+1)*(2*x-1)*(3*x+1)*(4*x-1)*(x+1)* (12*x^2-1)*(6*x^2-1)*(2*x^2-1)).