A371380 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^2 / (1-x) ).
1, 5, 46, 521, 6574, 88658, 1250920, 18236849, 272544886, 4153080950, 64284022516, 1007929418570, 15974993572732, 255522850658564, 4119461259700060, 66869059171095809, 1091990982773631910, 17927521032225339854, 295717190725184361364, 4898634803627227516238
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^2/(1-x))/x) -
PARI
a(n) = sum(k=0, n, 2^k*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(2*n+k+1,k) * binomial(2*n,n-k).