A223531 Triangle S(n,k) by rows: coefficients of 6^((n-1)/2)*(x^(1/6)*d/dx)^n when n=1,3,5,...

1, 7, 6, 91, 156, 36, 1729, 4446, 2052, 216, 43225, 148200, 102600, 21600, 1296, 1339975, 5742750, 5301000, 1674000, 200880, 7776, 49579075, 254978100, 294205500, 123876000, 22297680, 1726272, 46656, 2131900225, 12791401350, 17711171100, 9321669000

Offset

1,2

Links

Table of n, a(n) for n=1..32.

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;
7, 6;
91, 156, 36;
1729, 4446, 2052, 216;
43225, 148200, 102600, 21600, 1296;
1339975, 5742750, 5301000, 1674000, 200880, 7776;
49579075, 254978100, 294205500, 123876000, 22297680, 1726272, 46656;
2131900225, 12791401350, 17711171100, 9321669000, 2237200560, 259803936, 14043456, 279936;

Maple

a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(6^((i+1)mod 2)*x^((4((i+1)mod 2)+1)/6)*(diff(a[i-1], x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j-1];
end do;

Crossrefs

Odd rows of A223172.

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

Sequence in context: A038272 A249992 A366225 * A130553 A284210 A371078

Adjacent sequences: A223528 A223529 A223530 * A223532 A223533 A223534

Keyword

nonn,tabl

Author

Udita Katugampola, Mar 23 2013

Status

approved