A368467 - OEIS

%I #25 Feb 10 2024 14:02:47

%S 1,2,2,-16,-126,-498,-880,3432,37762,175916,411502,-710752,-12482928,

%T -66911830,-190616760,70959984,4208145282,26042918836,86794308524,

%U 50521487200,-1397839172626,-10176550581570,-38838971577536,-51156092490048,443929768322704

%N a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(4*n,n-k).

%F a(n) = [x^n] ( (1-x)^2 * (1+x)^4 )^n.

%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x/((1-x)^2*(1+x)^4) ). See A369190.

%o (PARI) a(n) = sum(k=0, n, (-1)^k * binomial(2*n, k)*binomial(4*n, n-k));

%Y Cf. A234839, A370106.

%Y Cf. A369190.

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 10 2024