A326474 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, 1, 2, 1, 0, 1, 22, 3, 1, 0, 1, 170, 63, 4, 1, 0, 1, 1366, 2187, 124, 5, 1, 0, 1, 10922, 59535, 7732, 205, 6, 1, 0, 1, 87382, 1594323, 599548, 18485, 306, 7, 1, 0, 1, 699050, 43033599, 39945364, 2416045, 36126, 427, 8, 1

Offset: 0

Author

Peter Luschny, Jul 08 2019

Keywords

• nonn
• tabl

Examples

			Array starts:
[0] 1, 0,   0,     0,       0,          0,            0, ... A000007
[1] 1, 1,   1,     1,       1,          1,            1, ... A000012
[2] 1, 2,  22,   170,    1366,      10922,        87382, ... A007613
[3] 1, 3,  63,  2187,   59535,    1594323,     43033599, ...
[4] 1, 4, 124,  7732,  599548,   39945364,   2556712828, ...
[5] 1, 5, 205, 18485, 2416045,  352060805,  46660373965, ...
[6] 1, 6, 306, 36126, 6673266, 1544907006, 379696000626, ...
      A051874,
		

Crossrefs

Rows include: A000007, A000012, A007613.

Columns include: A051874.

Cf. A326476 (m=2, p>=0), A326327 (m=2, p<=0), this sequence (m=3, p>=0), A326475 (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))