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

1, 1, 6, -2, 9, 8, 6, 13, 36, 36, -42, 70, -75, 180, 108, 798, -1162, 945, -630, 1620, 648, 3192, -4284, 3052, -1575, 630, -2268, -648, 92568, -117684, 77588, -35637, 12600, -1512, 18144, 3888, 1573656

Offset: 1

Author

Udita Katugampola, Apr 18 2013

Keywords

• sign
• tabl

Comments

These are generalized Stirling numbers.

Examples

			1;
1, 6;
-2, 9, 8;
6, 13, 36, 36;
-42, 70, -75, 180, 108;
798, -1162, 945, -630, 1620, 648;
		

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^(1/6)*(diff(a[i-1],x$1)))
end do;

Formula

G.f.: exp(((1+5/6*x*y)^(6/5)-1)/x).