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A223172 Triangle S(n,k) by rows: coefficients of 6^((n-1)/2))*(x^(1/6)*d/dx)^n when n is odd, and of 6^(n/2)*(x^(5/6)*d/dx)^n when n is even. 32
1, 1, 6, 7, 6, 7, 84, 36, 91, 156, 36, 91, 1638, 1404, 216, 1729, 4446, 2052, 216, 1729, 41496, 53352, 16416, 1296, 43225, 148200, 102600, 21600, 1296, 43225, 1296750, 2223000, 1026000, 162000, 7776, 1339975, 5742750, 5301000, 1674000, 200880, 7776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..40.

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 [math.CA], 2014.

EXAMPLE

Triangle begins:

        1;

        1,        6;

        7,        6;

        7,       84,        36;

       91,      156,        36;

       91,     1638,      1404,      216;

     1729,     4446,      2052,      216;

     1729,    41496,     53352,    16416,     1296;

    43225,   148200,    102600,    21600,     1296;

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

  1339975,  5742750,   5301000,  1674000,   200880,    7776;

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

MAPLE

a[0]:= f(x):

for i from 1 to 13 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;

CROSSREFS

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

Sequence in context: A010723 A244588 A336002 * A340153 A115096 A132957

Adjacent sequences:  A223169 A223170 A223171 * A223173 A223174 A223175

KEYWORD

nonn,tabf

AUTHOR

Udita Katugampola, Mar 20 2013

STATUS

approved

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Last modified July 27 15:29 EDT 2021. Contains 346307 sequences. (Running on oeis4.)