A145921 -id:A145921 - cp's OEIS frontend

A256194 a(n) = denominator of n!n^nProduct_{k=0..n} 1/(n*k + n - 1).

15, 440, 21945, 277704, 178986115, 215289360, 107174712645, 2019114114160, 5162399729063577, 310327149656160, 264020420256172514935, 555320997799108800, 183986274976015448239875, 7616449380979972355121376, 132186242095677958872242925, 3493664585524176681103200

Offset: 2

Michel Marcus, Mar 19 2015

n!*n^n*Product_{k=0..n} 1/(n*k + n - 1) = Sum_{k=0..n} (-1)^k*binomial(n,k)/(n*k + n - 1) (see arXiv link).

Brett Pansano, An Interesting Identity, arXiv:1503.04678 [math.GM], 2015.

Cf. A145921 (numerators).

Table[Denominator[n! n^n Product[1/(n k + n - 1), {k, 0, n}]], {n, 2, 17}] (* Jean-François Alcover, Sep 26 2018 *)

a(n) = denominator(sum(k=0, n, (-1)^k*binomial(n,k)/(n*k+n-1)));

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

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Aug 04 2023

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

Denominators are A145921.

Cf. A002596, A067622, A344745, A364660.

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

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

cp's OEIS Frontend

A256194 a(n) = denominator of n!n^nProduct_{k=0..n} 1/(n*k + n - 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

cp's OEIS Frontend

A256194 a(n) = denominator of n!*n^n*Product_{k=0..n} 1/(n*k + n - 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

A256194 a(n) = denominator of n!n^nProduct_{k=0..n} 1/(n*k + n - 1).