A274869 Number of set partitions of [n] into exactly five 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, 2, 13, 26, 113, 226, 833, 1666, 5649, 11298, 36561, 73122, 230161, 460322, 1424401, 2848802, 8720657, 17441314, 53021969, 106043938, 320925969, 641851938, 1936736529, 3873473058, 11665150225, 23330300450, 70169841937, 140339683874, 421734846737

Offset: 5

Author

Alois P. Heinz, Jul 09 2016

Keywords

• nonn
• easy

Examples

			a(6) = 2: 1|26|3|4|5, 1|2|3|46|5.
a(7) = 13: 13|24|5|6|7, 15|24|3|6|7, 1|24|35|6|7, 15|26|3|4|7, 15|2|3|46|7, 1|26|35|4|7, 1|2|35|46|7, 17|26|3|4|5, 1|26|37|4|5, 1|26|3|4|57, 17|2|3|46|5, 1|2|37|46|5, 1|2|3|46|57.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000

Crossrefs

Column k=5 of A274537.

Formula

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