OFFSET
1,2
LINKS
Marko Riedel, How many ways to get an odd number of each color in each bin?, Mathematics 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
KEYWORD
nonn
AUTHOR
Peter Kagey, Apr 15 2018
EXTENSIONS
More terms from Vaclav Kotesovec, Apr 16 2018
STATUS
approved