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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
1, 1, 4, 5, 40, 16, 45, 540, 432, 64, 585, 9360, 11232, 3328, 256, 9945, 198900, 318240, 141440, 21760, 1024, 208845, 5012280, 10024560, 5940480, 1370880, 129024, 4096, 5221125, 146191500, 350859600, 259896000, 79968000, 11289600, 716800, 16384, 151412625 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..37.

U. N. Katugampola, Mellin Transforms of Generalized Fractional Integrals and Derivatives, Appl. Math. Comput. 257(2015) 566-580.

U. N. Katugampola, Existence and Uniqueness results for a class of Generalized Fractional Differential Equations, arXiv preprint arXiv:1411.5229, 2014

EXAMPLE

Triangle begins:

1;

1, 4;

5, 40, 16;

45, 540, 432, 64;

585, 9360, 11232, 3328, 256;

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

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

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

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

MAPLE

a[0]:= f(x):

for i from 1 to 20 do

a[i] := simplify(4^((i+1)mod 2)*x^((2((i+1)mod 2)+1)/4)*(diff(a[i-1], x$1 )));

end do:

for j from 1 to 10 do

b[j]:=a[2j];

end do;

CROSSREFS

Even rows of A223170.

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

Sequence in context: A265689 A270098 A271285 * A189744 A241279 A245696

Adjacent sequences:  A223525 A223526 A223527 * A223529 A223530 A223531

KEYWORD

nonn,tabl

AUTHOR

Udita Katugampola, Mar 23 2013

STATUS

approved

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Last modified June 13 18:45 EDT 2021. Contains 345008 sequences. (Running on oeis4.)