A370836 Expansion of (1/x) * Series_Reversion( x/(x+1/(1+x^2)) ).
1, 1, 0, -2, -2, 6, 19, 1, -98, -170, 268, 1464, 967, -7253, -19035, 11497, 142894, 186814, -592148, -2327480, -371472, 14922592, 30367918, -44517534, -291059645, -242260229, 1550840094, 4611423196, -2050694753, -36095033685, -54276040088, 150373292998
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1+x^2)))/x) -
PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(n, 2*k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n,2*k) * binomial(3*k,k)/(2*k+1).