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

5,2

Links

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

Formula

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

Example

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.

Crossrefs

Column k=5 of A274537.

Sequence in context: A018745 A117983 A367265 * A018400 A091052 A294555

Adjacent sequences: A274866 A274867 A274868 * A274870 A274871 A274872

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 09 2016

Status

approved