A349271 Array A(n, k) that generalizes Euler numbers, class numbers, and tangent numbers, read by ascending antidiagonals.
1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 4, 8, 11, 5, 2, 4, 16, 46, 57, 16, 1, 6, 30, 128, 352, 361, 61, 2, 8, 46, 272, 1280, 3362, 2763, 272, 2, 8, 64, 522, 3522, 16384, 38528, 24611, 1385, 2, 12, 96, 904, 7970, 55744, 249856, 515086, 250737, 7936
Offset: 1
Examples
Seen as an array: [1] 1, 1, 1, 2, 5, 16, 61, 272, ... [A000111] [2] 1, 1, 3, 11, 57, 361, 2763, 24611, ... [A001586] [3] 1, 2, 8, 46, 352, 3362, 38528, 515086, ... [A007289] [4] 1, 4, 16, 128, 1280, 16384, 249856, 4456448, ... [A349264] [5] 2, 4, 30, 272, 3522, 55744, 1066590, 23750912, ... [A349265] [6] 2, 6, 46, 522, 7970, 152166, 3487246, 93241002, ... [A001587] [7] 1, 8, 64, 904, 15872, 355688, 9493504, 296327464, ... [A349266] [8] 2, 8, 96, 1408, 29184, 739328, 22634496, 806453248, ... [A349267] [9] 2, 12, 126, 2160, 49410, 1415232, 48649086, 1951153920, ... [A349268] . Seen as a triangle: [1] 1; [2] 1, 1; [3] 1, 1, 1; [4] 1, 2, 3, 2; [5] 2, 4, 8, 11, 5; [6] 2, 4, 16, 46, 57, 16; [7] 1, 6, 30, 128, 352, 361, 61; [8] 2, 8, 46, 272, 1280, 3362, 2763, 272; [9] 2, 8, 64, 522, 3522, 16384, 38528, 24611, 1385;
Links
- William Y. C. Chen, Neil J. Y. Fan, and Jeffrey Y. T. Jia, The generating function for the Dirichlet series Lm(s), Mathematics of Computation, Vol. 81, No. 278, pp. 1005-1023, April 2012.
- Ruth Lawrence and Don Zagier, Modular forms and quantum invariants of 3-manifolds, Asian J. Math. 3 (1999), no. 1, 93-107.
- D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967) 689-694.
- D. Shanks, Corrigendum: Generalized Euler and class numbers, Math. Comp. 22, (1968) 699.
- D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]