A274874 Number of set partitions of [n] into exactly ten 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, 5, 95, 475, 5294, 26470, 227294, 1136470, 8351711, 41758555, 277114769, 1385573845, 8568214932, 42841074660, 251848578952, 1259242894760, 7132223195725, 35661115978625, 196428153720067, 982140768600335, 5296485323226634, 26482426616133170

Offset: 10

Author

Alois P. Heinz, Jul 09 2016

Keywords

• nonn
• easy

Examples

			a(10) = 1: 1|2|3|4|5|6|7|8|9|(10).
a(11) = 5: 1(11)|2|3|4|5|6|7|8|9|(10), 1|2|3(11)|4|5|6|7|8|9|(10), 1|2|3|4|5(11)|6|7|8|9|(10), 1|2|3|4|5|6|7(11)|8|9|(10), 1|2|3|4|5|6|7|8|9(11)|(10).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..1000

Crossrefs

Column k=10 of A274537.

Formula

G.f.: -x^10/((x-1)*(4*x+1)*(3*x-1)*(5*x-1)*(2*x+1)*(2*x-1)*(3*x+1)*(4*x-1)*(x+1)*(12*x^2-1)*(6*x^2-1)*(20*x^2-1)*(2*x^2-1)).