A349271 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,8

LINKS

Table of n, a(n) for n=1..55.

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).

Rows: A000111, A001586, A007289, A349265, A001587, A349266, A349267, A349268.

Columns: A000003 (class numbers), A000061, A000233, A000176, A000362, A000488, A000508, A000518.

Cf. A349263 (main diagonal).

Sequence in context: A292588 A335965 A225176 * A349387 A118665 A333238

Adjacent sequences: A349268 A349269 A349270 * A349272 A349273 A349274

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Nov 23 2021

STATUS

approved