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A223536 Coefficients of (x^(1/6)*d/dx)^n for positive integer n.

%I A223536 #25 Jun 24 2017 01:11:29
%S A223536 1,1,6,-2,9,8,6,13,36,36,-42,70,-75,180,108,798,-1162,945,-630,1620,
%T A223536 648,3192,-4284,3052,-1575,630,-2268,-648,92568,-117684,77588,-35637,
%U A223536 12600,-1512,18144,3888,1573656
%N A223536 Coefficients of (x^(1/6)*d/dx)^n for positive integer n.
%C A223536 These are generalized Stirling numbers.
%H A223536 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 A223536 G.f.: exp(((1+5/6*x*y)^(6/5)-1)/x).
%e A223536 1;
%e A223536 1, 6;
%e A223536 -2, 9, 8;
%e A223536 6, 13, 36, 36;
%e A223536 -42, 70, -75, 180, 108;
%e A223536 798, -1162, 945, -630, 1620, 648;
%p A223536 # This will generate the sequence as coefficients of pseudo polynomials
%p A223536 # up to a constant multiple.
%p A223536 a[0] := f(x):
%p A223536 for i to 10 do
%p A223536 a[i] := simplify(x^(1/6)*(diff(a[i-1],x$1)))
%p A223536 end do;
%Y A223536 Cf. A223168-A223172, A223533-A223536.
%K A223536 sign,tabl
%O A223536 1,3
%A A223536 _Udita Katugampola_, Apr 18 2013