login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A223171 Triangle S(n,k) by rows: coefficients of 5^((n-1)/2))*(x^(1/5)*d/dx)^n when n is odd, and of 5^(n/2)*(x^(4/5)*d/dx)^n when n is even. 2
1, 1, 5, 6, 5, 6, 60, 25, 66, 110, 25, 66, 990, 825, 125, 1056, 2640, 1200, 125, 1056, 21120, 26400, 8000, 625, 22176, 73920, 50400, 10500, 625, 22176, 554400, 924000, 420000, 65625, 3125, 576576, 2402400, 2184000, 682500, 81250, 3125, 576576, 17297280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..42.

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, 5;

6, 60, 25;

66, 110, 25;

66, 990, 825, 125;

1056, 2640, 1200, 125;

1056, 21120, 26400, 8000, 625;

22176, 73920, 50400, 10500, 625;

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

576576, 2402400, 2184000, 682500, 81250, 3125;

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

17873856, 89369280, 101556000, 42315000, 7556250, 581250, 15625;

MAPLE

a[0]:= f(x):

for i from 1 to 13 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;

CROSSREFS

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

Sequence in context: A139396 A010487 A177957 * A188942 A011258 A217177

Adjacent sequences:  A223168 A223169 A223170 * A223172 A223173 A223174

KEYWORD

nonn,tabf

AUTHOR

Udita Katugampola, Mar 20 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 December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)