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URL: https://oeis.org/A344745

⇱ A344745 - OEIS

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A344745
Numerators of generalized binomial coefficients (-1/k choose k).
1
-1, 3, -14, 195, -924, 267995, -164604, 45886995, -519348280, 843061472253, -33644021190, 19713207603254165, -29447897812956, 7112683552535920515, -219530334327028402216, 2896662162807666940995, -59209706525969052144, 63061212713478261338180955809, -124888410979403015484540
OFFSET
1,2
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
EXAMPLE
The fractions are -1, 3/8, -14/81, 195/2048, -924/15625, 267995/6718464, -164604/5764801, 45886995/2147483648, -519348280/31381059609, 843061472253/64000000000000, ...
MATHEMATICA
a[n_] := Numerator @ Binomial[-1/n, n]; Array[a, 20] (* Amiram Eldar, May 28 2021 *)
PROG
(PARI) a(n) = numerator(binomial(-1/n, n)); \\ Michel Marcus, Jun 15 2021
CROSSREFS
Cf. A344746 (denominators).
Sequence in context: A288559 A366715 A132490 * A058388 A362385 A327230
KEYWORD
sign,frac
AUTHOR
Chris Grossack, May 28 2021
STATUS
approved