A371430 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4 - x^2) ).
1, 4, 21, 128, 851, 5984, 43759, 329396, 2535406, 19863592, 157874971, 1269833668, 10316765299, 84540929568, 697928139977, 5799156785376, 48461097907978, 407020852551016, 3434002483872566, 29090171931564848, 247333930963224287, 2109921586071433064
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4-x^2))/x) -
PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, k)*binomial(4*n-4*k+4, n-2*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,k) * binomial(4*n-4*k+4,n-2*k).