A372037 G.f. A(x) satisfies A(x) = ( 1 + 4*x*(1 + x)*A(x) )^(1/2).
1, 2, 4, 4, 0, -8, -8, 16, 48, 0, -192, -256, 480, 1792, 320, -7808, -12544, 19200, 87808, 33280, -382464, -720896, 854016, 4870144, 2844160, -20553728, -44909568, 38967296, 289456128, 228986880, -1163309056, -2932514816, 1701978112, 17951686656, 17979965440
Offset: 0
Keywords
Crossrefs
Cf. A372035.
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(1/(-2*x*(1+x)+sqrt(1+(2*x*(1+x))^2))) -
PARI
a(n) = sum(k=0, n, 4^k*binomial(k/2+1/2, k)*binomial(k, n-k)/(k+1));
Formula
G.f.: A(x) = 1/(-2*x*(1+x) + sqrt(1+(2*x*(1+x))^2)).
a(n) = Sum_{k=0..n} 4^k * binomial(k/2+1/2,k) * binomial(k,n-k)/(k+1).