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

%I #14 Sep 08 2022 08:45:48

%S 1,1,-2,20,-504,25200,-2189088,302702400,-62564261760,18427508985600,

%T -7449695786856960,4010313259477324800,-2803674333549374208000,

%U 2492728196309155284480000,-2768630339381333070099456000

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

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

%H Vincenzo Librandi, <a href="/A168136/b168136.txt">Table of n, a(n) for n = 0..100</a>

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

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

%o (Magma) [Bernoulli(2*n)*Factorial(2*n+1)/Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Jul 14 2016

%Y Cf. A001332, A004193.

%K sign

%O 0,3

%A _Franklin T. Adams-Watters_, Nov 19 2009