A223533 -id:A223533 - cp's OEIS frontend

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

Udita Katugampola, Apr 18 2013

These are generalized Stirling numbers.

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

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

Cf. A223168-A223172, A223533-A223536.

# 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;

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

A223534 Coefficients of (x^(1/4)*d/dx)^n for n positive integer.

Original entry on oeis.org

1, 1, 4, -1, 6, 8, 5, -10, 48, 32, -10, 15, -10, 80, 32, 110, -145, 90, 40, 480, 128, -770, 945, -560, 140, 560, 1344, 256, -13090, 15365, -8820, 2940, -6272, -7168, -1024, 65450, -74550, 41825, -14700, 2940, -13440, -9216, -1024, 1505350, -1678250, 925575

Offset: 1

Udita Katugampola, Apr 18 2013

These are generalized Stirling numbers.

			1;
1, 4;
-1, 6, 8;
5, -10, 48, 32;
-10, 15, -10, 80, 32;
110, -145, 90, 40, 480, 128;
-770, 945, -560, 140, 560, 1344, 256;

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

Cf. A223168-A223172, A223533-A223536.

# 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^(1/4)*(diff(a[i-1],x$1)))
end do;

G.f.: exp(((1+3/4*x*y)^(4/3)-1)/x).

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

Original entry on oeis.org

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

Udita Katugampola, Apr 18 2013

These are generalized Stirling numbers.

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

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

Cf. A223168-A223172, A223533-A223536.

# 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;

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

cp's OEIS Frontend

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

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A223534 Coefficients of (x^(1/4)*d/dx)^n for n positive integer.

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Maple

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

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Formula