A368467 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(4*n,n-k).
1, 2, 2, -16, -126, -498, -880, 3432, 37762, 175916, 411502, -710752, -12482928, -66911830, -190616760, 70959984, 4208145282, 26042918836, 86794308524, 50521487200, -1397839172626, -10176550581570, -38838971577536, -51156092490048, 443929768322704
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-1)^k * binomial(2*n, k)*binomial(4*n, n-k));
Formula
a(n) = [x^n] ( (1-x)^2 * (1+x)^4 )^n.
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.