A223532 - OEIS

A223532

Triangle S(n,k) by rows: coefficients of 6^(n/2)*(x^(5/6)*d/dx)^n when n=0,2,4,6,...

1, 1, 6, 7, 84, 36, 91, 1638, 1404, 216, 1729, 41496, 53352, 16416, 1296, 43225, 1296750, 2223000, 1026000, 162000, 7776, 1339975, 48239100, 103369500, 63612000, 15066000, 1446336, 46656, 49579075, 2082321150, 5354540100, 4118877000, 1300698000, 187300512

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..34.

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, 6;

7, 84, 36;

91, 1638, 1404, 216;

1729, 41496, 53352, 16416, 1296;

43225, 1296750, 2223000, 1026000, 162000, 7776;

1339975, 48239100, 103369500, 63612000, 15066000, 1446336, 46656;

49579075, 2082321150, 5354540100, 4118877000, 1300698000, 187300512, 12083904, 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];

end do;

CROSSREFS

Even rows of A223172.

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

Sequence in context: A219517 A232008 A156791 * A041081 A041082 A036417

Adjacent sequences: A223529 A223530 A223531 * A223533 A223534 A223535

KEYWORD

nonn,tabl

AUTHOR

Udita Katugampola, Mar 23 2013

STATUS

approved

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