|
%I #24 Aug 14 2015 21:15:04
%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
|
