A370841 Expansion of (1/x) * Series_Reversion( x * (1/(1-x^4) - x) ).
1, 1, 2, 5, 13, 35, 96, 264, 719, 1914, 4888, 11583, 23540, 29907, -57120, -695742, -3938275, -18266657, -76983710, -306116660, -1168987469, -4327878214, -15617536020, -55097816085, -190320077663, -643865817117, -2131713980560, -6893257768141
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1-x^4)-x))/x) -
PARI
a(n) = sum(k=0, n\4, (-1)^k*binomial(2*n-4*k+1, k)*binomial(2*n-4*k, n-4*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(2*n-4*k+1,k) * binomial(2*n-4*k,n-4*k).