A048833 Number of starting positions of Nim with 2n pieces such that 2nd player wins. Partitions of 2n such that xor-sum of partitions is 0.

1, 1, 2, 4, 6, 10, 16, 31, 43, 68, 98, 153, 213, 317, 443, 704, 971, 1415, 1975, 2818, 3865, 5401, 7366, 10142, 13639, 18438, 24583, 32861, 43345, 57268, 75175, 99119, 129278, 168796, 219614, 284887, 368546, 475919, 614379, 788845, 1012117