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A349271
Array A(n, k) that generalizes Euler numbers, class numbers, and tangent numbers, read by ascending antidiagonals.
8
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
1,8
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]
EXAMPLE
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;
CROSSREFS
A235605 (array generalized Euler secant numbers).
A235606 (array generalized Euler tangent numbers).
A349264 (overview generating functions).
Columns: A000003 (class numbers), A000061, A000233, A000176, A000362, A000488, A000508, A000518.
Cf. A349263 (main diagonal).
Sequence in context: A292588 A335965 A225176 * A349387 A118665 A333238
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 23 2021
STATUS
approved