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 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 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

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Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)