A364713 - OEIS

%I #12 Aug 05 2023 06:25:59

%S 1,-1,5,-77,399,-124729,81549,-23960365,283583443,-478398640447,

%T 19740912828,-11911591259019739,18262332208600,-4514446693068714225,

%U 142267808222130386191,-1912831808055538077885,39773048560156838355,-43025628065750129034887540875,86435429204640847578555

%N a(n) is the numerator of coefficient of x^n in expansion of (1 + x)^(1/n).

%e 1, -1/8, 5/81, -77/2048, 399/15625, -124729/6718464, 81549/5764801, ...

%t Table[SeriesCoefficient[(1 + x)^(1/n), {x, 0, n}], {n, 1, 21}] // Numerator

%t Table[Binomial[1/n, n], {n, 1, 21}] // Numerator

%o (PARI) a(n) = numerator(binomial(1/n, n)); \\ _Michel Marcus_, Aug 05 2023

%Y Denominators are A145921.

%Y Cf. A002596, A067622, A344745, A364660.

%K sign,frac

%O 1,3

%A _Ilya Gutkovskiy_, Aug 04 2023