A326475 A(n, k) = (m*k)! [x^k] MittagLefflerE(m, x)^(-n), for m = 3, n >= 0, k >= 0; square array read by descending antidiagonals.

1, 0, 1, 0, -1, 1, 0, 19, -2, 1, 0, -1513, 58, -3, 1, 0, 315523, -6218, 117, -4, 1, 0, -136085041, 1630330, -15795, 196, -5, 1, 0, 105261234643, -847053482, 4997781, -31924, 295, -6, 1, 0, -132705221399353, 766492673914, -3042574083, 11840836, -56285, 414, -7, 1

Offset: 0

Author

Peter Luschny, Jul 08 2019

Keywords

• sign
• tabl

Examples

			Array starts:
[0] 1,  0,   0,      0,        0,            0, ... A000007
[1] 1, -1,  19,  -1513,   315523,   -136085041, ... A002115
[2] 1, -2,  58,  -6218,  1630330,   -847053482, ...
[3] 1, -3, 117, -15795,  4997781,  -3042574083, ...
[4] 1, -4, 196, -31924, 11840836,  -8271354004, ...
[5] 1, -5, 295, -56285, 23952055, -18889306805, ...
[6] 1, -6, 414, -90558, 43493598, -38227720446, ...
		

Crossrefs

Rows: A000007, A002115.

Cf. A326476 (m=2, p>=0), A326327 (m=2, p<=0), A326474 (m=3, p>=0), this sequence (m=3, p<=0).

Programs

Mathematica

(* The function MLPower is defined in A326327. *)
For[n = 0, n < 8, n++, Print[MLPower[3, -n, 8]]]

Sage

# uses[MLPower from A326327]
for n in (0..6): print(MLPower(3, -n, 9))