A326476 A(n, k) = (m*k)! [x^k] MittagLefflerE(m, x)^n, for m = 2, n >= 0, k >= 0; square array read by descending antidiagonals.

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 8, 3, 1, 0, 1, 32, 21, 4, 1, 0, 1, 128, 183, 40, 5, 1, 0, 1, 512, 1641, 544, 65, 6, 1, 0, 1, 2048, 14763, 8320, 1205, 96, 7, 1, 0, 1, 8192, 132861, 131584, 26465, 2256, 133, 8, 1, 0, 1, 32768, 1195743, 2099200, 628805, 64896, 3787, 176, 9, 1

Offset

0,9

Links

Table of n, a(n) for n=0..65.

Example

Array starts:
[0] 1, 0,   0,    0,      0,        0,          0,            0, ... A000007
[1] 1, 1,   1,    1,      1,        1,          1,            1, ... A000012
[2] 1, 2,   8,   32,    128,      512,       2048,         8192, ... A081294
[3] 1, 3,  21,  183,   1641,    14763,     132861,      1195743, ... A054879
[4] 1, 4,  40,  544,   8320,   131584,    2099200,     33562624, ... A092812
[5] 1, 5,  65, 1205,  26465,   628805,   15424865,    382964405, ... A121822
[6] 1, 6,  96, 2256,  64896,  2086656,   71172096,   2499219456, ...
[7] 1, 7, 133, 3787, 134953,  5501167,  243147373,  11266376947, ...
[8] 1, 8, 176, 5888, 250496, 12397568,  676591616,  39316226048, ...
[9] 1, 9, 225, 8649, 427905, 24943689, 1624354785, 114066126729, ...
      A000567,
Seen as a triangle:
[1]
[0, 1]
[0, 1, 1]
[0, 1, 2, 1]
[0, 1, 8, 3, 1]
[0, 1, 32, 21, 4, 1]
[0, 1, 128, 183, 40, 5, 1]
[0, 1, 512, 1641, 544, 65, 6, 1]
[0, 1, 2048, 14763, 8320, 1205, 96, 7, 1]
[0, 1, 8192, 132861, 131584, 26465, 2256, 133, 8, 1]

Mathematica

(* The function MLPower is defined in A326327. *)
For[n = 0, n < 8, n++, Print[MLPower[2, n, 8]]]

Prog

(Sage) # uses[MLPower from A326327]
for n in (0..6): print(MLPower(2, n, 9))

Crossrefs

Rows include: A000007, A000012, A081294, A054879, A092812, A121822.

Columns include: A000567. Variant: A286899.

Cf. A326474 (m=3, p>=0), A326475 (m=3, p<=0), A326327 (m=2, p<=0), this sequence (m=2, p>=0).

Sequence in context: A058998 A085324 A264945 * A247864 A370398 A331278

Adjacent sequences: A326473 A326474 A326475 * A326477 A326478 A326479

Keyword

nonn,tabl

Author

Peter Luschny, Jul 08 2019

Status

approved