A364713 a(n) is the numerator of coefficient of x^n in expansion of (1 + x)^(1/n).

1, -1, 5, -77, 399, -124729, 81549, -23960365, 283583443, -478398640447, 19740912828, -11911591259019739, 18262332208600, -4514446693068714225, 142267808222130386191, -1912831808055538077885, 39773048560156838355, -43025628065750129034887540875, 86435429204640847578555

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Example

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

Mathematica

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

Prog

(PARI) a(n) = numerator(binomial(1/n, n)); \\ Michel Marcus, Aug 05 2023

Crossrefs

Denominators are A145921.

Cf. A002596, A067622, A344745, A364660.

Sequence in context: A059856 A001513 A028556 * A214867 A330999 A331000

Adjacent sequences: A364710 A364711 A364712 * A364714 A364715 A364716

Keyword

sign,frac

Author

Ilya Gutkovskiy, Aug 04 2023

Status

approved