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A219557 Sum of numbers of bipartite partitions of (n,k) into distinct pairs for 0<=k<=n. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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

EXAMPLE

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)].

CROSSREFS

Row sums of A201377.

Sequence in context: A344247 A333770 A281973 * A094538 A343735 A037129

Adjacent sequences:  A219554 A219555 A219556 * A219558 A219559 A219560

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 22 2012

STATUS

approved

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)