A168136 a(n) = Bernoulli(2n)*(2n+1)!/n!.

1, 1, -2, 20, -504, 25200, -2189088, 302702400, -62564261760, 18427508985600, -7449695786856960, 4010313259477324800, -2803674333549374208000, 2492728196309155284480000, -2768630339381333070099456000

Offset: 0

Author

Franklin T. Adams-Watters, Nov 19 2009

Keywords

• sign

Comments

Given by alternating sums of coefficients of polynomials spawned by sums of binomial(n,k)^2*k^(2m). - John M. Campbell, Nov 30 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A001332, A004193.

Programs

Magma

[Bernoulli(2*n)*Factorial(2*n+1)/Factorial(n): n in [0..20]]; // Vincenzo Librandi, Jul 14 2016

Mathematica

Table[BernoulliB[2*n]*(2*n+1)!/n!, {n, 0, 20}]

PARI

a(n)=bernfrac(2*n)*(2*n+1)!/n!