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.

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

Offset: 1

Author

Peter Kagey, Apr 15 2018

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

Cf. A090806, A108469.

Programs

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 *)

Extensions

More terms from Vaclav Kotesovec, Apr 16 2018