A102463 a(n) is the number of distinct values of (Sum_{i=1..r} x_i)!/(Product_{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, 1, 2, 3, 4, 6, 8, 11, 13, 18, 21, 30, 33, 40, 49, 58, 68, 79, 94, 110, 128, 149, 168, 197, 217, 253, 282, 328, 360, 421, 452, 520, 567, 652, 692, 812, 868, 980, 1053, 1188, 1278, 1449, 1545, 1731, 1837, 2081, 2185, 2457, 2598, 2901, 3062, 3421, 3603, 4002, 4200
Offset: 1
Keywords
Examples
a(4) = 3 because the 5 tuples (0, 0, 0, 1), (1, 0, 1), (0, 2), (2, 1) and (4) yield three different values, 1, 2 and 3: 1!/1! = 1, 2!/1!*1! = 2, 2!/2! = 1, 3!/2!*1! = 3 and 4!/4! = 1.
Extensions
More terms and better description from David Wasserman, Apr 07 2008
Comments