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

0,9

Links

Table of n, a(n) for n=0..54.

Example

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,

Mathematica

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

Prog

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

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).

Sequence in context: A062154 A359619 A334159 * A266886 A267546 A228817

Adjacent sequences: A326471 A326472 A326473 * A326475 A326476 A326477

Keyword

nonn,tabl

Author

Peter Luschny, Jul 08 2019

Status

approved