cp's OEIS Frontend

A223535 Coefficients of (x^(1/5)*d/dx)^n for positive integer n.

%I A223535 #24 Jun 24 2017 01:22:29
%S A223535 1,1,5,-3,15,25,21,-45,150,125,-231,375,-375,1250,625,693,-981,750,
%T A223535 -375,1875,625,-13167,17199,-11655,5250,13125,3125,302841,-375417,
%U A223535 237510,-100275,26250,26250,87500,15625,8176707,-9773379,5914755,-2390850,685125,-78750
%N A223535 Coefficients of (x^(1/5)*d/dx)^n for positive integer n.
%C A223535 These are generalized Stirling numbers.
%H A223535 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 A223535 G.f.: exp(((1+4/5*x*y)^(5/4)-1)/x).
%e A223535 1;
%e A223535 1, 5;
%e A223535 -3, 15, 25;
%e A223535 21, -45, 150, 125;
%e A223535 -231, 375, -375, 1250, 625;
%e A223535 693, -981, 750, -375, 1875, 625;
%p A223535 # This will generate the sequence as coefficients of pseudo polynomials
%p A223535 # up to a constant multiple.
%p A223535 a[0] := f(x):
%p A223535 for i to 10 do
%p A223535 a[i] := simplify(x^(1/5)*(diff(a[i-1],x$1)))
%p A223535 end do;
%Y A223535 Cf. A223168-A223172, A223533-A223536.
%K A223535 sign,tabl
%O A223535 1,3
%A A223535 _Udita Katugampola_, Apr 18 2013