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A223534 Coefficients of (x^(1/4)*d/dx)^n for n positive integer.

%I A223534 #24 Jun 24 2017 01:17:15
%S A223534 1,1,4,-1,6,8,5,-10,48,32,-10,15,-10,80,32,110,-145,90,40,480,128,
%T A223534 -770,945,-560,140,560,1344,256,-13090,15365,-8820,2940,-6272,-7168,
%U A223534 -1024,65450,-74550,41825,-14700,2940,-13440,-9216,-1024,1505350,-1678250,925575
%N A223534 Coefficients of (x^(1/4)*d/dx)^n for n positive integer.
%C A223534 These are generalized Stirling numbers.
%H A223534 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 A223534 G.f.: exp(((1+3/4*x*y)^(4/3)-1)/x).
%e A223534 1;
%e A223534 1, 4;
%e A223534 -1, 6, 8;
%e A223534 5, -10, 48, 32;
%e A223534 -10, 15, -10, 80, 32;
%e A223534 110, -145, 90, 40, 480, 128;
%e A223534 -770, 945, -560, 140, 560, 1344, 256;
%p A223534 # This will generate the sequence as coefficients of pseudo polynomials
%p A223534 # up to a constant multiple.
%p A223534 a[0] := f(x):
%p A223534 for i to 10 do
%p A223534 a[i] := simplify(x^(1/4)*(diff(a[i-1],x$1)))
%p A223534 end do;
%Y A223534 Cf. A223168-A223172, A223533-A223536.
%K A223534 sign,tabl
%O A223534 1,3
%A A223534 _Udita Katugampola_, Apr 18 2013