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 A219555 Number of bipartite partitions of (i,j) with i+j = n into distinct pairs. 10
 1, 2, 4, 10, 19, 38, 73, 134, 242, 430, 749, 1282, 2171, 3622, 5979, 9770, 15802, 25334, 40288, 63560, 99554, 154884, 239397, 367800, 561846, 853584, 1290107, 1940304, 2904447, 4328184, 6422164, 9489940, 13967783, 20480534, 29920277, 43557272, 63194864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 (first 100 terms from Alois P. Heinz) FORMULA a(n) = Sum_{i+j=n} [x^i*y^j] 1/2 * Product_{k,m>=0} (1+x^k*y^m). G.f.: Product_{k>=1} (1+x^k)^(k+1). - Vaclav Kotesovec, Mar 07 2015 a(n) ~ Zeta(3)^(1/6) * exp(-Pi^4 / (1296*Zeta(3)) + Pi^2 * n^(1/3) / (2^(5/3) * 3^(4/3) * Zeta(3)^(1/3)) + (3/2)^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(5/4) * 3^(1/3) * sqrt(Pi) * n^(2/3)), where Zeta(3) = A002117. - Vaclav Kotesovec, Mar 07 2015 G.f.: exp(Sum_{k>=1} (-1)^(k+1)*x^k*(2 - x^k)/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, Aug 11 2018 EXAMPLE a(2) = 4: [(2,0)], [(1,1)], [(1,0),(0,1)], [(0,2)]. MATHEMATICA nmax=50; CoefficientList[Series[Product[(1+x^k)^(k+1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2015 *) CROSSREFS Row sums of A054242. Cf. A026007, A052812, A005380, A255834, A255836. Sequence in context: A253772 A043330 A295961 * A263738 A011963 A083844 Adjacent sequences:  A219552 A219553 A219554 * A219556 A219557 A219558 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 22 2012 STATUS approved

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Last modified July 22 07:23 EDT 2019. Contains 325216 sequences. (Running on oeis4.)