A371394 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+3*x)^3 ).
1, 10, 137, 2174, 37562, 686004, 13027065, 254641398, 5089756958, 103552330700, 2137385941418, 44647634773420, 942085264713556, 20050276273007080, 429913404536172633, 9278142975370425510, 201383222768034837750, 4393265621094818733660
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+3*x)^3)/x) -
PARI
a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(3*(n+1),k) * binomial(2*n-k,n-k).