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A223533 Coefficients of (x^(1/3)*d/dx)^n for positive integer n.

%I A223533 #25 Jun 24 2017 01:13:44
%S A223533 1,1,3,-1,9,9,1,-1,18,9,-5,5,15,90,27,35,-35,225,405,81,-105,105,-35,
%T A223533 630,567,81,1155,-1155,490,-105,4158,2268,243,15015,-15015,6895,945,
%U A223533 -10206,-23814,-8748,-729,75075,-75075,35700,-10675,2835,-945,34020,41310,10935,729
%N A223533 Coefficients of (x^(1/3)*d/dx)^n for positive integer n.
%C A223533 These are generalized Stirling numbers.
%H A223533 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 A223533 G.f.: exp(((1+2/3*x*y)^(3/2)-1)/x).
%e A223533 1;
%e A223533 1, 3;
%e A223533 -1, 9, 9;
%e A223533 1, -1, 18, 9;
%e A223533 -5, 5, 15, 90, 27;
%e A223533 35, -35, 225, 405, 81;
%e A223533 -105, 105, 630, 567, -35, 81;
%e A223533 1155, -1155, 630, 4158, 490, 2268, -105, 243;
%p A223533 # This will generate the sequence as coefficients of pseudo polynomials
%p A223533 # up to a constant multiple.
%p A223533 a[0] := f(x):
%p A223533 for i to 10 do
%p A223533 a[i] := simplify(x^(1/3)*(diff(a[i-1],x$1)))
%p A223533 end do;
%Y A223533 Cf. A223168-A223172, A223534-A223536.
%K A223533 sign,tabl
%O A223533 1,3
%A A223533 _Udita Katugampola_, Apr 18 2013