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A219557 Sum of numbers of bipartite partitions of (n,k) into distinct pairs for 0<=k<=n. 2

%I

%S 1,3,9,33,96,273,749,1953,4916,12023,28642,66575,151544,338294,741880,

%T 1601048,3403936,7137386,14774713,30219025,61115184,122300146,

%U 242312186,475589389,925158391,1784529840,3414565313,6483608230,12221370425,22876263089,42534593868

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

%H Alois P. Heinz, <a href="/A219557/b219557.txt">Table of n, a(n) for n = 0..80</a>

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

%e 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)].

%Y Row sums of A201377.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Nov 22 2012

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Last modified January 17 13:51 EST 2022. Contains 350396 sequences. (Running on oeis4.)