A223533 Coefficients of (x^(1/3)*d/dx)^n for positive integer n.
1, 1, 3, -1, 9, 9, 1, -1, 18, 9, -5, 5, 15, 90, 27, 35, -35, 225, 405, 81, -105, 105, -35, 630, 567, 81, 1155, -1155, 490, -105, 4158, 2268, 243, 15015, -15015, 6895, 945, -10206, -23814, -8748, -729, 75075, -75075, 35700, -10675, 2835, -945, 34020, 41310, 10935, 729
Offset: 1
Examples
1; 1, 3; -1, 9, 9; 1, -1, 18, 9; -5, 5, 15, 90, 27; 35, -35, 225, 405, 81; -105, 105, 630, 567, -35, 81; 1155, -1155, 630, 4158, 490, 2268, -105, 243;
Links
- U. N. Katugampola, Mellin Transforms of Generalized Fractional Integrals and Derivatives, Appl. Math. Comput. 257(2015) 566-580.
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^(1/3)*(diff(a[i-1],x$1))) end do;
Formula
G.f.: exp(((1+2/3*x*y)^(3/2)-1)/x).
Comments