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A223528 Triangle S(n,k) by rows: coefficients of 4^(n/2)*(x^(3/4)*d/dx)^n when n=0,2,4,6,... 0

%I

%S 1,1,4,5,40,16,45,540,432,64,585,9360,11232,3328,256,9945,198900,

%T 318240,141440,21760,1024,208845,5012280,10024560,5940480,1370880,

%U 129024,4096,5221125,146191500,350859600,259896000,79968000,11289600,716800,16384,151412625

%N Triangle S(n,k) by rows: coefficients of 4^(n/2)*(x^(3/4)*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.

%H U. N. Katugampola, <a href="http://arxiv.org/abs/1411.5229">Existence and Uniqueness results for a class of Generalized Fractional Differential Equations</a>, arXiv preprint arXiv:1411.5229, 2014

%e Triangle begins:

%e 1;

%e 1, 4;

%e 5, 40, 16;

%e 45, 540, 432, 64;

%e 585, 9360, 11232, 3328, 256;

%e 9945, 198900, 318240, 141440, 21760, 1024;

%e 208845, 5012280, 10024560, 5940480, 1370880, 129024, 4096;

%e 5221125, 146191500, 350859600, 259896000, 79968000, 11289600, 716800, 16384;

%e 151412625, 4845204000, 13566571200, 12059174400, 4638144000, 873062400, 83148800, 3801088, 65536;

%p a[0]:= f(x):

%p for i from 1 to 20 do

%p a[i] := simplify(4^((i+1)mod 2)*x^((2((i+1)mod 2)+1)/4)*(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 rows of A223170.

%Y Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

%K nonn,tabl

%O 1,3

%A _Udita Katugampola_, Mar 23 2013

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Last modified July 31 06:15 EDT 2021. Contains 346369 sequences. (Running on oeis4.)