%I #4 Mar 15 2015 17:35:58
%S 1,4,2,9,24,5,20,84,54,132,15,35,240,320,630,780,720,52,66,570,870,
%T 2280,465,6240,4440,1320,8280,4050,203,105,1260,1974,6720,2394,20580,
%U 19740,14385,11445,83160,31080,34860,77910,23772,877,176,2520,4312,17640,5432
%N Refines A075197(n): number of partitions of n balls of n colors. The refinement has shape A000041(n).
%C a(n) can be calculated by resorting A035206 into Mathematica order vice AS1 ordering and then multiplying term by term with A096443(n).
%e The array begins
%e 1
%e 4 2
%e 9 24 5
%e 20 84 54 132 15
%e ...
%e Row three is (9,24,5) because there are (3, 4,5) cases; and we have (3, 6,1) ways to pick 1,2 or 3 colors.
%Y Cf. A000041, A000110, A035206, A075197, A096443, A114994.
%K nonn
%O 1,2
%A _Alford Arnold_, May 19 2007