A344745 Numerators of generalized binomial coefficients (-1/k choose k).

-1, 3, -14, 195, -924, 267995, -164604, 45886995, -519348280, 843061472253, -33644021190, 19713207603254165, -29447897812956, 7112683552535920515, -219530334327028402216, 2896662162807666940995, -59209706525969052144, 63061212713478261338180955809, -124888410979403015484540

Offset: 1

Author

Chris Grossack, May 28 2021

Keywords

• sign
• frac

Examples

			The fractions are -1, 3/8, -14/81, 195/2048, -924/15625, 267995/6718464, -164604/5764801, 45886995/2147483648, -519348280/31381059609, 843061472253/64000000000000, ...
		

Crossrefs

Cf. A344746 (denominators).

Programs

Mathematica

a[n_] := Numerator @ Binomial[-1/n, n]; Array[a, 20] (* Amiram Eldar, May 28 2021 *)

PARI

a(n) = numerator(binomial(-1/n, n)); \\ Michel Marcus, Jun 15 2021

Formula

a(k) = numerator of binomial(-1/k, k).

a(n) is the numerator of coefficient of x^n in expansion of (1 + x)^(-1/n). - Ilya Gutkovskiy, Aug 04 2023