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A302919 The number of ways of placing 2n-1 white balls and 2n-1 black balls into unlabeled bins such that each bin has both an odd number of white balls and black balls. 0
1, 2, 4, 12, 32, 85, 217, 539, 1316, 3146, 7374, 16969, 38387, 85452, 187456, 405659, 866759, 1830086, 3821072, 7894447, 16148593, 32723147, 65719405, 130871128, 258513076, 506724988, 985968770, 1904992841, 3655873294, 6970687150, 13208622956, 24879427889, 46593011280, 86773920240, 160742462714, 296227087942, 543183754454, 991213989213 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..38.

Marko Riedel, How many ways to get an odd number of each color in each bin?, Math Stack Exchange.

EXAMPLE

For n = 3 the a(3) = 4 ways to place five white and five black balls are (wwwwwbbbbb), (wwwbbb)(wb)(wb), (wwwb)(wbbb)(wb), and (wb)(wb)(wb)(wb)(wb).

MATHEMATICA

nmax = 15; p = 1; Do[Do[p = Expand[p*(1 - x^(2*i - 1)*y^(2*j - 1))]; p = Select[p, (Exponent[#, x] <= 2*nmax - 1) && (Exponent[#, y] <= 2*nmax - 1) &], {i, 1, 2*nmax - 1}], {j, 1, nmax}]; p = Expand[Normal[Series[1/p, {x, 0, 2*nmax - 1}, {y, 0, 2*nmax - 1}]]]; p = Select[p, Exponent[#, x] == Exponent[#, y] &]; Flatten[{1, Table[Coefficient[p, x^(2*n - 1)*y^(2*n - 1)], {n, 1, nmax}]}] (* Vaclav Kotesovec, Apr 16 2018 *)

CROSSREFS

Cf. A090806, A108469.

Sequence in context: A323864 A242659 A109388 * A181329 A293007 A028860

Adjacent sequences:  A302916 A302917 A302918 * A302920 A302921 A302922

KEYWORD

nonn

AUTHOR

Peter Kagey, Apr 15 2018

EXTENSIONS

More terms from Vaclav Kotesovec, Apr 16 2018

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)