A223535 Coefficients of (x^(1/5)*d/dx)^n for positive integer n.

1, 1, 5, -3, 15, 25, 21, -45, 150, 125, -231, 375, -375, 1250, 625, 693, -981, 750, -375, 1875, 625, -13167, 17199, -11655, 5250, 13125, 3125, 302841, -375417, 237510, -100275, 26250, 26250, 87500, 15625, 8176707, -9773379, 5914755, -2390850, 685125, -78750

Offset: 1

Author

Udita Katugampola, Apr 18 2013

Keywords

• sign
• tabl

Comments

These are generalized Stirling numbers.

Examples

			1;
1, 5;
-3, 15, 25;
21, -45, 150, 125;
-231, 375, -375, 1250, 625;
693, -981, 750, -375, 1875, 625;
		

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^(1/5)*(diff(a[i-1],x$1)))
end do;

Formula

G.f.: exp(((1+4/5*x*y)^(5/4)-1)/x).