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A383453
The Geode Bi-Tri infinite rectangular array, read by upward antidiagonals.
6
1, 2, 3, 5, 16, 12, 14, 70, 110, 55, 42, 288, 702, 728, 273, 132, 1155, 3850, 6160, 4760, 1428, 429, 4576, 19448, 42432, 50388, 31008, 7752, 1430, 18018, 93366, 259350, 418950, 395010, 201894, 43263, 4862, 70720, 433160, 1466080, 3010700, 3853696, 3010700, 1315600, 246675
OFFSET
0,2
LINKS
N. J. Wildberger and Dean Rubine, A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode, Amer. Math. Monthly (2025).
FORMULA
The entry (m2, m3) of the rectangular array is equal to (2*m2 + 3*m3 + 3)!/((2*m2 + 2*m3 + 3)*(m2 + m3 + 1)*(m2 + 2*m3 + 2)! * m2! * m3!), with m2, m3 >= 0.
EXAMPLE
The array begins:
1, 3, 12, 55, 273, 1428, ...
2, 16, 110, 728, 4760, 31008, ...
5, 70, 702, 6160, 50388, 395010, ...
14, 288, 3850, 42432, 418950, 3853696, ...
42, 1155, 19448, 259350, 3010700, 31870410, ...
132, 4576, 93366, 1466080, 19612560, 235282320, ...
429, 18018, 433160, 7845024, 119041650, 1598394798, ...
1430, 70720, 1961256, 40310400, 685026342, 10189625600, ...
...
The first few antidiagonals are:
[ 1],
[ 2, 3],
[ 5, 16, 12],
[ 14, 70, 110, 55],
[ 42, 288, 702, 728, 273],
[132, 1155, 3850, 6160, 4760, 1428],
[429, 4576, 19448, 42432, 50388, 31008, 7752],
...
CROSSREFS
Same table as A243660, transposed. - Dan Eilers, May 06 2025
The leading row and column of the rectangular array are A001764 and A000108.
See A383454-A383457 for other rows and columns.
Sequence in context: A248827 A273525 A377853 * A274336 A192648 A219339
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 02 2025
STATUS
approved