A369631 Expansion of (1/x) * Series_Reversion( x * (1/(1+x^4) - x) ).
1, 1, 2, 5, 15, 49, 168, 594, 2149, 7920, 29640, 112359, 430564, 1665197, 6491280, 25478886, 100611695, 399421439, 1593221090, 6382176160, 25664184349, 103560846454, 419215870860, 1701907025715, 6927658961599, 28268225980197, 115608889788304
Offset: 0
Keywords
Programs
-
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, 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)} binomial(2*n-4*k+1,k) * binomial(2*n-4*k,n-4*k).