A371406 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^2 ) ).
1, 6, 49, 462, 4734, 51216, 575705, 6657846, 78703438, 946740132, 11551512042, 142616584380, 1778372098000, 22365031140900, 283341912929865, 3612782260978470, 46326552943960278, 597034029166804068, 7728885814331709374, 100458438481544424996
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^2))/x) -
PARI
a(n) = sum(k=0, n, 2^k*binomial(2*(n+1), k)*binomial(2*(n+1), n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(2*(n+1),k) * binomial(2*(n+1),n-k).
a(n) = A219538(n+1)/2. - Seiichi Manyama, Dec 24 2024
a(n) = (1/(n+1)) * [x^n] ( (1+x) * (1+2*x) )^(2*(n+1)). - Seiichi Manyama, Dec 25 2024