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A096652
Lower triangular matrix T, read by rows, such that the row sums of T^n form the (2n)-dimensional partition numbers.
2
1, 0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 5, 5, 2, 1, 0, 7, 7, 7, 2, 1, 0, 11, 16, 9, 9, 2, 1, 0, 15, 15, 31, 11, 11, 2, 1, 0, 22, 59, -4, 54, 13, 13, 2, 1, 0, 30, -109, 313, -72, 87, 15, 15, 2, 1, 0, 42, 1314, -1922, 1122, -225, 132, 17, 17, 2, 1, 0, 56, -11804, 19468, -9671, 3087, -509, 191, 19, 19, 2, 1, 0, 77, 133957, -217176, 110734, -32581
OFFSET
0,5
COMMENTS
Row sums of T form A000219 (planar partitions); row sums of T^2 form A000334(4-D); row sums of T^3 form A000416(6-D).
FORMULA
Matrix square of triangle A096651.
EXAMPLE
Triangle T begins:
{1},
{0,1},
{0,2,1},
{0,3,2,1},
{0,5,5,2,1},
{0,7,7,7,2,1},
{0,11,16,9,9,2,1},
{0,15,15,31,11,11,2,1},
{0,22,59,-4,54,13,13,2,1},
{0,30,-109,313,-72,87,15,15,2,1},
{0,42,1314,-1922,1122,-225,132,17,17,2,1},
{0,56,-11804,19468,-9671,3087,-509,191,19,19,2,1},
{0,77,133957,-217176,110734,-32581,7137,-980,266,21,21,2,1},
{0,101,-1728760,2809257,-1426436,422732,-87714,14601,-1704,359,23,23,2,1},...
Row sums are: {1,1,3,6,13,24,48,86,160,282,500,859,...} (A000219).
T^2 begins:
{1},
{0,1},
{0,4,1},
{0,10,4,1},
{0,26,14,4,1},
{0,59,38,18,4,1},
{0,140,109,50,22,4,1},
{0,307,256,179,62,26,4,1},
{0,684,709,370,273,74,30,4,1},
{0,1464,1240,1683,438,395,86,34,4,1},...
with row sums: {1,1,5,15,45,120,326,835,2145,5345,...} (A000334).
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Jul 06 2004
STATUS
approved