A223527 Triangle S(n,k) by rows: coefficients of 4^((n-1)/2)*(x^(1/4)*d/dx)^n when n=1,3,5,...

1, 5, 4, 45, 72, 16, 585, 1404, 624, 64, 9945, 31824, 21216, 4352, 256, 208845, 835380, 742560, 228480, 26880, 1024, 5221125, 25061400, 27846000, 11424000, 2016000, 153600, 4096, 151412625, 847910700, 1130547600, 579768000, 136416000, 15590400, 831488, 16384

Offset

1,2

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;
5, 4;
45, 72, 16;
585, 1404, 624, 64;
9945, 31824, 21216, 4352, 256;
208845, 835380, 742560, 228480, 26880, 1024;
5221125, 25061400, 27846000, 11424000, 2016000, 153600, 4096;
151412625, 847910700, 1130547600, 579768000, 136416000, 15590400, 831488, 16384;

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-1];
end do;

Crossrefs

Odd rows of A223170.

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

Sequence in context: A123233 A189748 A304151 * A262421 A305170 A192344

Adjacent sequences: A223524 A223525 A223526 * A223528 A223529 A223530

Keyword

nonn,tabl

Author

Udita Katugampola, Mar 23 2013

Status

approved