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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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: A173591 A156603 A156612 * A072407 A061158 A180843

Adjacent sequences:  A096798 A096799 A096800 * A096802 A096803 A096804

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 13 2004

STATUS

approved

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Last modified March 30 04:35 EDT 2017. Contains 284296 sequences.