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

0,8

Comments

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.

Links

Table of n, a(n) for n=0..68.

Example

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],...

Crossrefs

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

Sequence in context: A368028 A342645 A350024 * A072407 A361999 A061158

Adjacent sequences: A096798 A096799 A096800 * A096802 A096803 A096804

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 13 2004

Status

approved