A371416 Expansion of (1/x) * Series_Reversion( x * (1 - 3*x - x^3) ).
1, 3, 18, 136, 1152, 10458, 99472, 978453, 9871686, 101590654, 1062271704, 11253818628, 120535386692, 1303045817184, 14199323523912, 155805565801803, 1720024043803542, 19090440094335912, 212897898182054224, 2384431948345110510, 26808516659219953680
Offset: 0
Keywords
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x-x^3))/x) -
PARI
a(n) = sum(k=0, n\2, 3^k*binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
-
PARI
a(n) = sum(k=0, n\3, 3^(n-3*k)*binomial(n+k, k)*binomial(2*n-2*k, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} 3^k * binomial(n+k,k) * binomial(4*n+k+2,n-2*k).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} 3^(n-3*k) * binomial(n+k,k) * binomial(2*n-2*k,n-3*k).