This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383453 #46 May 09 2025 15:07:32 %S A383453 1,2,3,5,16,12,14,70,110,55,42,288,702,728,273,132,1155,3850,6160, %T A383453 4760,1428,429,4576,19448,42432,50388,31008,7752,1430,18018,93366, %U A383453 259350,418950,395010,201894,43263,4862,70720,433160,1466080,3010700,3853696,3010700,1315600,246675 %N A383453 The Geode Bi-Tri infinite rectangular array, read by upward antidiagonals. %H A383453 N. J. Wildberger and Dean Rubine, <a href="https://doi.org/10.1080/00029890.2025.2460966">A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode</a>, Amer. Math. Monthly (2025). %F A383453 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. %e A383453 The array begins: %e A383453 1, 3, 12, 55, 273, 1428, ... %e A383453 2, 16, 110, 728, 4760, 31008, ... %e A383453 5, 70, 702, 6160, 50388, 395010, ... %e A383453 14, 288, 3850, 42432, 418950, 3853696, ... %e A383453 42, 1155, 19448, 259350, 3010700, 31870410, ... %e A383453 132, 4576, 93366, 1466080, 19612560, 235282320, ... %e A383453 429, 18018, 433160, 7845024, 119041650, 1598394798, ... %e A383453 1430, 70720, 1961256, 40310400, 685026342, 10189625600, ... %e A383453 ... %e A383453 The first few antidiagonals are: %e A383453 [ 1], %e A383453 [ 2, 3], %e A383453 [ 5, 16, 12], %e A383453 [ 14, 70, 110, 55], %e A383453 [ 42, 288, 702, 728, 273], %e A383453 [132, 1155, 3850, 6160, 4760, 1428], %e A383453 [429, 4576, 19448, 42432, 50388, 31008, 7752], %e A383453 ... %Y A383453 Same table as A243660, transposed. - _Dan Eilers_, May 06 2025 %Y A383453 The leading row and column of the rectangular array are A001764 and A000108. %Y A383453 See A383454-A383457 for other rows and columns. %K A383453 nonn,tabl %O A383453 0,2 %A A383453 _N. J. A. Sloane_, May 02 2025