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%I #25 Jun 24 2017 01:13:44
%S 1,1,3,-1,9,9,1,-1,18,9,-5,5,15,90,27,35,-35,225,405,81,-105,105,-35,
%T 630,567,81,1155,-1155,490,-105,4158,2268,243,15015,-15015,6895,945,
%U -10206,-23814,-8748,-729,75075,-75075,35700,-10675,2835,-945,34020,41310,10935,729
%N Coefficients of (x^(1/3)*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+2/3*x*y)^(3/2)-1)/x).
%e 1;
%e 1, 3;
%e -1, 9, 9;
%e 1, -1, 18, 9;
%e -5, 5, 15, 90, 27;
%e 35, -35, 225, 405, 81;
%e -105, 105, 630, 567, -35, 81;
%e 1155, -1155, 630, 4158, 490, 2268, -105, 243;
%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^(1/3)*(diff(a[i-1],x$1)))
%p end do;
%Y Cf. A223168-A223172, A223534-A223536.
%K sign,tabl
%O 1,3
%A _Udita Katugampola_, Apr 18 2013
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