A096801 Triangle, read by rows, that transforms the (n+m)-dimensional partitions of n into the (n+m+1)-dimensional partitions of n, for fixed m.
1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 7, 3, 1, 1, 0, 26, 10, 4, 1, 1, 0, 124, 44, 13, 5, 1, 1, 0, 640, 218, 68, 16, 6, 1, 1, 0, 3695, 1208, 332, 99, 19, 7, 1, 1, 0, 23231, 7403, 2100, 457, 138, 22, 8, 1, 1, 0, 156572, 48663, 12566, 3518, 579, 186, 25, 9, 1, 1, 0, 1133838, 346636
Offset: 0
Examples
The main diagonal of A096751: {1,1,3,10,45,216,...} (A096752),
is transformed into the secondary diagonal: {1,1,4,15,71,357,...},
as demonstrated by the dot product of row #5 with A096752:
[0,26,10,4,1,1]*[1,1,3,10,45,216] = 357.
Rows begin:
[1],
[0,1],
[0,1,1],
[0,2,1,1],
[0,7,3,1,1],
[0,26,10,4,1,1],
[0,124,44,13,5,1,1],
[0,640,218,68,16,6,1,1],
[0,3695,1208,332,99,19,7,1,1],
[0,23231,7403,2100,457,138,22,8,1,1],
[0,156572,48663,12566,3518,579,186,25,9,1,1],
[0,1133838,346636,94878,18043,5787,679,244,28,10,1,1],
[0,8635777,2590866,623351,188962,20539,9391,733,313,31,11,1,1],
[0,70212042,20875236,5828851,762072,398052,13238,15009,712,394,34,12,1,1],...
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