
EXAMPLE

The number of mdimensional partitions of 5, for m>=0, is given by the binomial transform of the 5th row:
BINOMIAL([1,6,11,7,1]) = [1,7,24,59,120,216,357,554,819,1165,...] = A008779.
Rows begin:
[1],
[1,1],
[1,2,1],
[1,4,4,1],
[1,6,11,7,1],
[1,10,27,28,11,1],
[1,14,57,93,64,16,1],
[1,21,117,269,282,131,22,1],
[1,29,223,707,1062,766,244,29,1],
[1,41,417,1747,3565,3681,1871,421,37,1],
[1,55,748,4090,10999,15489,11400,4152,683,46,1],
[1,76,1326,9219,31828,58975,59433,31802,8483,1054,56,1],
[1,100,2284,20095,87490,207735,276230,204072,80664,16162,1561,67,1],
[1,134,3898,42707,230737,687665,1173533,1148939,632478,188077,29031,2234,79,1],...
The inverse binomial transform of the diagonals of this triangle begin:
[1],
[1,1,1],
[1,3,4,6,3],
[1,5,16,29,49,45,15],
[1,9,38,127,289,540,660,420,105],
[1,13,90,397,1384,3633,7506,10920,9765,4725,945],
[1,20,182,1140,5266,19324,55645,125447,?,?,?,62370,10395],...
