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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

These are generalized Stirling numbers.

LINKS

Table of n, a(n) for n=1..51.

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

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

Cf. A223168-A223172, A223534-A223536.

Sequence in context: A016601 A193031 A078416 * A021973 A075498 A105729

Adjacent sequences:  A223530 A223531 A223532 * A223534 A223535 A223536

KEYWORD

sign,tabl

AUTHOR

Udita Katugampola, Apr 18 2013

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)