A102463 - OEIS

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.

%I #10 Jan 09 2021 10:16:10

%S 1,1,2,3,4,6,8,11,13,18,21,30,33,40,49,58,68,79,94,110,128,149,168,

%T 197,217,253,282,328,360,421,452,520,567,652,692,812,868,980,1053,

%U 1188,1278,1449,1545,1731,1837,2081,2185,2457,2598,2901,3062,3421,3603,4002,4200

%N 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.

%C The r-tuples correspond to the partitions of n and for each r-tuple, (Sum_{i=1..r} x_i)!/(Product_{i=1..r} x_i!) is the number of permutations of the corresponding partition. - _David Wasserman_, Apr 07 2008

%e 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.

%Y Cf. A102462, A102464, A102465.

%K nonn

%O 1,3

%A _Vladeta Jovovic_, Feb 23 2005

%E More terms and better description from _David Wasserman_, Apr 07 2008