A127974 Numerators in expansion of (1-x)^(-2/3).

1, 2, 5, 40, 110, 308, 2618, 7480, 21505, 559130, 1621477, 4717024, 41273960, 120646960, 353323240, 3109244512, 9133405754, 26862958100, 711868389650, 2098138411600, 6189508314220, 54821359354520, 161972198092900

Offset: 0

Author

Paul Barry, Feb 09 2007

Keywords

• easy
• nonn
• frac

Comments

Numerators of n!/A008544(n) are A127975.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001790, A008544, A104133, A127975.

Programs

Mathematica

Numerator[CoefficientList[Series[(1 - x)^(-2/3), {x, 0, 50}], x]] (* G. C. Greubel, May 07 2018 *)

Formula

a(n) = denominator(n!/A008544(n)).

a(n) = denominator(n!/(Product_{k=0..n-1} (2+3*k))).

Conjecture: a(n-1) = the numerator of (1/(2*sqrt(3)*Pi)) * Integral_{x >= 0} 1/(1 + x^3)^n. - Peter Bala, Jun 11 2024