A219557 Sum of numbers of bipartite partitions of (n,k) into distinct pairs for 0<=k<=n.

1, 3, 9, 33, 96, 273, 749, 1953, 4916, 12023, 28642, 66575, 151544, 338294, 741880, 1601048, 3403936, 7137386, 14774713, 30219025, 61115184, 122300146, 242312186, 475589389, 925158391, 1784529840, 3414565313, 6483608230, 12221370425, 22876263089, 42534593868

Offset: 0

Author

Alois P. Heinz, Nov 22 2012

Keywords

• nonn

Examples

			a(2) = 9: [(2,0)], [(2,1)], [(2,0),(0,1)], [(1,1),(1,0)], [(2,2)], [(2,1),(0,1)], [(2,0),(0,2)], [(1,2),(1,0)], [(1,1),(1,0),(0,1)].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80

Crossrefs

Row sums of A201377.

Formula

a(n) = Sum_{k=0..n} [x^n*y^k] 1/2 * Product_{i,j>=0} (1+x^i*y^j).