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Coefficients of (x^(1/5)*d/dx)^n for positive integer n.
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%I #24 Jun 24 2017 01:22:29

%S 1,1,5,-3,15,25,21,-45,150,125,-231,375,-375,1250,625,693,-981,750,

%T -375,1875,625,-13167,17199,-11655,5250,13125,3125,302841,-375417,

%U 237510,-100275,26250,26250,87500,15625,8176707,-9773379,5914755,-2390850,685125,-78750

%N Coefficients of (x^(1/5)*d/dx)^n for positive integer n.

%C These are generalized Stirling numbers.

%H U. N. Katugampola, <a href="http://authors.elsevier.com/a/1QhUNLvMg0Zs~">Mellin Transforms of Generalized Fractional Integrals and Derivatives</a>, Appl. Math. Comput. 257(2015) 566-580.

%F G.f.: exp(((1+4/5*x*y)^(5/4)-1)/x).

%e 1;

%e 1, 5;

%e -3, 15, 25;

%e 21, -45, 150, 125;

%e -231, 375, -375, 1250, 625;

%e 693, -981, 750, -375, 1875, 625;

%p # This will generate the sequence as coefficients of pseudo polynomials

%p # up to a constant multiple.

%p a[0] := f(x):

%p for i to 10 do

%p a[i] := simplify(x^(1/5)*(diff(a[i-1],x$1)))

%p end do;

%Y Cf. A223168-A223172, A223533-A223536.

%K sign,tabl

%O 1,3

%A _Udita Katugampola_, Apr 18 2013