A371434 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x^2) ).
1, 3, 14, 76, 444, 2702, 16840, 106389, 676566, 4307754, 27333384, 172040544, 1068547788, 6505380072, 38446578888, 217095119499, 1136270066490, 5125578859296, 15040187738184, -47786768551830, -1453703259770520, -18311261482519860, -186896777677695720
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3+x^2))/x) -
PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+k,k) * binomial(4*n+k+2,n-2*k).