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A223533
Coefficients of (x^(1/3)*d/dx)^n for positive integer n.
3
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
1,3
COMMENTS
These are generalized Stirling numbers.
LINKS
FORMULA
G.f.: exp(((1+2/3*x*y)^(3/2)-1)/x).
EXAMPLE
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;
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;
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Udita Katugampola, Apr 18 2013
STATUS
approved