A371366 Expansion of (1/x) * Series_Reversion( x * (1-5*x)^2 / (1-4*x) ).
1, 6, 71, 1046, 17231, 303876, 5611556, 107128046, 2097177071, 41870595806, 849284396751, 17451906690856, 362539208779396, 7601087206512096, 160635649725455256, 3418231465333316126, 73178876192536066031, 1575035438677302619746
Offset: 0
Keywords
Crossrefs
Cf. A078009.
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-5*x)^2/(1-4*x))/x) -
PARI
a(n) = sum(k=0, n, 4^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 4^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).