A371427 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 - x^4) ).
1, 2, 5, 14, 41, 122, 363, 1066, 3046, 8300, 20791, 43738, 51297, -174406, -1825027, -10480330, -50143510, -218385772, -895007802, -3504952380, -13214355159, -48116028934, -169216483595, -573113441834, -1856620607526, -5675964306988, -15927363432481
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2-x^4))/x) -
PARI
a(n) = sum(k=0, n\4, (-1)^k*binomial(n+1, k)*binomial(2*n-2*k+2, n-4*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+1,k) * binomial(2*n-2*k+2,n-4*k).