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

1, 1, 4, -1, 6, 8, 5, -10, 48, 32, -10, 15, -10, 80, 32, 110, -145, 90, 40, 480, 128, -770, 945, -560, 140, 560, 1344, 256, -13090, 15365, -8820, 2940, -6272, -7168, -1024, 65450, -74550, 41825, -14700, 2940, -13440, -9216, -1024, 1505350, -1678250, 925575

Offset: 1

Author

Udita Katugampola, Apr 18 2013

Keywords

• sign
• tabl

Comments

These are generalized Stirling numbers.

Examples

			1;
1, 4;
-1, 6, 8;
5, -10, 48, 32;
-10, 15, -10, 80, 32;
110, -145, 90, 40, 480, 128;
-770, 945, -560, 140, 560, 1344, 256;
		

Links

• U. N. Katugampola, Mellin Transforms of Generalized Fractional Integrals and Derivatives, Appl. Math. Comput. 257(2015) 566-580.

Crossrefs

Cf. A223168-A223172, A223533-A223536.

Programs

Maple

# This will generate the sequence as coefficients of pseudo polynomials
# up to a constant multiple.
a[0] := f(x):
for i to 10 do
a[i] := simplify(x^(1/4)*(diff(a[i-1],x$1)))
end do;

Formula

G.f.: exp(((1+3/4*x*y)^(4/3)-1)/x).