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

%I #20 May 18 2022 09:36:18

%S 1,1,-1,4,-36,600,-16584,705600,-43751232,3790108800,-443539877760,

%T 68218849036800,-13478425925184000,3355402067989171200,

%U -1035218714714606822400,390189256983139461120000,-177430554756972746695065600,96269372301568677170319360000

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

%H Robert Israel, <a href="/A263445/b263445.txt">Table of n, a(n) for n = 0..210</a>

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

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

%F a(n) ~ (-1)^(n+1)*8*sqrt(2)*n^3*(n/e)^(3*n)*Pi^(1-2*n). - _Vladimir Reshetnikov_, Sep 05 2016

%p seq((2*n+1)*(n+1)!*bernoulli(2*n), n=0..50); # _Robert Israel_, Oct 18 2015

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

%o (PARI) vector(30, n, n--; (2*n+1)*(n+1)!*bernfrac(2*n)) \\ _Altug Alkan_, Oct 18 2015

%o (Python)

%o from math import factorial

%o from sympy import bernoulli

%o def A263445(n): return (2*n+1)*factorial(n+1)*bernoulli(2*n) # _Chai Wah Wu_, May 18 2022

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

%K sign

%O 0,4

%A _Vladimir Reshetnikov_, Oct 18 2015