A344745 - OEIS

%I #23 Aug 04 2023 10:12:34

%S -1,3,-14,195,-924,267995,-164604,45886995,-519348280,843061472253,

%T -33644021190,19713207603254165,-29447897812956,7112683552535920515,

%U -219530334327028402216,2896662162807666940995,-59209706525969052144,63061212713478261338180955809,-124888410979403015484540

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

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

%F a(n) is the numerator of coefficient of x^n in expansion of (1 + x)^(-1/n). - _Ilya Gutkovskiy_, Aug 04 2023

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

%t a[n_] := Numerator @ Binomial[-1/n, n]; Array[a, 20] (* _Amiram Eldar_, May 28 2021 *)

%o (PARI) a(n) = numerator(binomial(-1/n, n)); \\ _Michel Marcus_, Jun 15 2021

%Y Cf. A344746 (denominators).

%K sign,frac

%O 1,2

%A _Chris Grossack_, May 28 2021