login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A223530 Triangle S(n,k) by rows: coefficients of 5^(n/2)*(x^(4/5)*d/dx)^n when n=0,2,4,6,... 0
1, 1, 5, 6, 60, 25, 66, 990, 825, 125, 1056, 21120, 26400, 8000, 625, 22176, 554400, 924000, 420000, 65625, 3125, 576576, 17297280, 36036000, 21840000, 5118750, 487500, 15625, 17873856, 625584960, 1563962400, 1184820000, 370256250, 52893750, 3390625, 78125 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..36.

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, 5;

6, 60, 25;

66, 990, 825, 125;

1056, 21120, 26400, 8000, 625;

22176, 554400, 924000, 420000, 65625, 3125;

576576, 17297280, 36036000, 21840000, 5118750, 487500, 15625;

17873856, 625584960, 1563962400, 1184820000, 370256250, 52893750, 3390625, 78125;

MAPLE

a[0]:= f(x):

for i from 1 to 20 do

a[i] := simplify(5^((i+1)mod 2)*x^((3((i+1)mod 2)+1)/5)*(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 A223171.

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

Sequence in context: A256291 A299243 A191557 * A132444 A111504 A041057

Adjacent sequences:  A223527 A223528 A223529 * A223531 A223532 A223533

KEYWORD

nonn,tabl

AUTHOR

Udita Katugampola, Mar 23 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)