A263445 a(n) = (2n+1)*(n+1)!*Bernoulli(2n).

1, 1, -1, 4, -36, 600, -16584, 705600, -43751232, 3790108800, -443539877760, 68218849036800, -13478425925184000, 3355402067989171200, -1035218714714606822400, 390189256983139461120000, -177430554756972746695065600, 96269372301568677170319360000

Offset: 0

Author

Vladimir Reshetnikov, Oct 18 2015

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..210
• Index entries for sequences related to Bernoulli numbers.

Crossrefs

Bernoulli numbers are A000367/A002445. Cf. A004193, A001332, A000182, A001469.

Programs

Maple

seq((2*n+1)*(n+1)!*bernoulli(2*n), n=0..50); # Robert Israel, Oct 18 2015

Mathematica

Table[(2n + 1) (n + 1)! BernoulliB[2n], {n, 0, 17}]

PARI

vector(30, n, n--; (2*n+1)*(n+1)!*bernfrac(2*n)) \\ Altug Alkan, Oct 18 2015

Python

from math import factorial
from sympy import bernoulli
def A263445(n): return (2*n+1)*factorial(n+1)*bernoulli(2*n) # Chai Wah Wu, May 18 2022

Formula

a(n) = (2n+1)*(n+1)!*Bernoulli(2n).

a(n) ~ (-1)^(n+1)*8*sqrt(2)*n^3*(n/e)^(3*n)*Pi^(1-2*n). - Vladimir Reshetnikov, Sep 05 2016