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%I #25 Mar 15 2015 16:55:29
%S 1,1,3,4,24,9,28,252,189,27,280,3360,3780,1080,81,3640,54600,81900,
%T 35100,5265,243,58240,1048320,1965600,1123200,252720,23328,729,
%U 1106560,23237760,52284960,37346400,11203920,1551312,96957,2187,24344320,584263680,1533692160
%N Triangle S(n,k) by rows: coefficients of 3^(n/2)*(x^(2/3)*d/dx)^n when n=0,2,4,6,...
%H U. N. Katugampola, <a href="http://authors.elsevier.com/a/1QhUNLvMg0Zs~">Mellin Transforms of Generalized Fractional Integrals and Derivatives</a>, Appl. Math. Comput. 257(2015) 566-580.
%F T(n,0) = A007559(n) and T(n,n) = A000244(n) for all n>=0
%e Triangle begins:
%e 1;
%e 1, 3;
%e 4, 24, 9;
%e 28, 252, 189, 27;
%e 280, 3360, 3780, 1080, 81;
%e 3640, 54600, 81900, 35100, 5265, 243;
%e 58240, 1048320, 1965600, 1123200, 252720, 23328, 729;
%e 1106560, 23237760, 52284960, 37346400, 11203920, 1551312, 96957, 2187;
%e 24344320, 584263680, 1533692160, 1314593280, 492972480, 91010304, 8532216, 384912, 6561;
%p a[0]:= f(x):
%p for i from 1 to 20 do
%p a[i] := simplify(3^((i+1)mod 2)*x^(((i+1)mod 2+1)/3)*(diff(a[i-1],x$1 )));
%p end do:
%p for j from 1 to 10 do
%p b[j]:=a[2j];
%p end do;
%Y Even row of A223169.
%Y Cf. A223168-A223172, A223511-A223532.
%K nonn,tabl
%O 1,3
%A _Udita Katugampola_, Mar 18 2013
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