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%I #14 Mar 24 2020 03:41:52
%S 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,
%T 0,1,10922,59535,7732,205,6,1,0,1,87382,1594323,599548,18485,306,7,1,
%U 0,1,699050,43033599,39945364,2416045,36126,427,8,1
%N A(n, k) = (m*k)! [x^k] MittagLefflerE(m, x)^n, for m = 3, n >= 0, k >= 0; square array read by descending antidiagonals.
%e Array starts:
%e [0] 1, 0, 0, 0, 0, 0, 0, ... A000007
%e [1] 1, 1, 1, 1, 1, 1, 1, ... A000012
%e [2] 1, 2, 22, 170, 1366, 10922, 87382, ... A007613
%e [3] 1, 3, 63, 2187, 59535, 1594323, 43033599, ...
%e [4] 1, 4, 124, 7732, 599548, 39945364, 2556712828, ...
%e [5] 1, 5, 205, 18485, 2416045, 352060805, 46660373965, ...
%e [6] 1, 6, 306, 36126, 6673266, 1544907006, 379696000626, ...
%e A051874,
%t (* The function MLPower is defined in A326327. *)
%t For[n = 0, n < 8, n++, Print[MLPower[3, n, 8]]]
%o (Sage) # uses[MLPower from A326327]
%o for n in (0..6): print(MLPower(3, n, 9))
%Y Rows include: A000007, A000012, A007613.
%Y Columns include: A051874.
%Y Cf. A326476 (m=2, p>=0), A326327 (m=2, p<=0), this sequence (m=3, p>=0), A326475 (m=3, p<=0).
%K nonn,tabl
%O 0,9
%A _Peter Luschny_, Jul 08 2019
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