A102464 a(n) = number of distinct values of prod_{i=1..r} x_i!, where (x_1, ..., x_r) is an r-tuple of nonnegative integers with sum_{i=1..r} i*x_i = n.

1, 2, 2, 3, 4, 6, 7, 10, 12, 14, 16, 21, 23, 28, 32, 39, 44, 52, 59, 69, 79, 89, 96, 112, 124, 144, 154, 177, 190, 219, 237, 264, 288, 322, 344, 398, 421, 471, 505, 558, 598, 672, 711, 787, 842, 930, 975, 1081, 1149, 1248, 1335, 1453, 1533, 1676, 1768, 1933, 2046