_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jul 13 2004

nonn,tabl,new

Paul D . Hanna (pauldhanna(AT)juno.com), Jul 13 2004

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

0,8

Transforms any diagonal of A096751 (square table of n-dimensional partitions) into the next lower diagonal in the table. It is not yet certain if this triangle contains negative terms.

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],...

Cf. A096751, A096752, A096802 (row sums), A096803-A096805 (columns).

nonn,tabl

Paul D Hanna (pauldhanna(AT)juno.com), Jul 13 2004

approved