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A219555 Number of bipartite partitions of (i,j) with i+j = n into distinct pairs. 9
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

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 January 20 02:29 EST 2018. Contains 297938 sequences.