A102465 a(n) = number of distinct values of prod_{i=1..r} x_i!*i!^x_i, where (x_1, ..., x_r) is an r-tuple of nonnegative integers with sum_{i=1..r} i*x_i = n.

1, 1, 2, 4, 4, 7, 7, 13, 17, 23, 26, 40, 45, 60, 64, 102, 115, 148, 169, 225, 261, 337, 375, 470, 552, 668, 780, 954, 1078, 1331, 1469, 1811, 2055, 2475, 2776, 3343, 3764, 4447, 4983, 5898, 6622, 7771, 8646, 10192, 11403, 13238, 14680, 17011, 19010, 21877