A107661 Array read by antidiagonals: T(n,m) = Sum m^max(k,n-k),k=0..n.
1, 1, 2, 1, 4, 3, 1, 6, 10, 4, 1, 8, 21, 24, 5, 1, 10, 36, 72, 52, 6, 1, 12, 55, 160, 225, 112, 7, 1, 14, 78, 300, 656, 702, 232, 8, 1, 16, 105, 504, 1525, 2688, 2133, 480, 9, 1, 18, 136, 784, 3060, 7750, 10816, 6480, 976, 10, 1, 20, 171, 1152, 5537, 18576, 38875
Offset: 0
Examples
The array starts in row n=0 and column m=1 as:
1, 1, 1, 1, 1, 1,...
2, 4, 6, 8, 10, 12,...
3, 10, 21, 36, 55, 78,...
4, 24, 72, 160, 300, 504,...
5, 52, 225, 656, 1525, 3060,...
6, 112, 702, 2688, 7750,18576,...
7, 232, 2133,10816,38875,111672,...
8, 480, 6480,43520,195000,671328,...
Formula
a(2n) = m^n(2(m^(n+1)-1)/(m-1)-1), a(2n+1) = 2m^(n+1)(m^(n+1)-1)/(m-1)
T(5,m) = m^2*(2*m^2+2*m+1). - R. J. Mathar, Aug 16 2013