A379522 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^3 * (1+2*x)^3 ) ).
1, 9, 114, 1683, 27111, 462060, 8192078, 149541975, 2791795695, 53056724409, 1023021616920, 19963667407572, 393536736830724, 7824888965728584, 156750391932619254, 3160558799674447167, 64092227061832430895, 1306327265854324847595, 26746550927141536784370
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3*(1+2*x)^3))/x) -
PARI
a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(3*(n+1), n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(3*(n+1),n-k).
a(n) = (1/(n+1)) * [x^n] ( (1+x) * (1+2*x) )^(3*(n+1)).