A371392 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+2*x)^3 ).
1, 7, 68, 769, 9492, 124014, 1686120, 23610565, 338200148, 4932348226, 72993007672, 1093371638954, 16545598769416, 252567107648604, 3884497559034192, 60136704175071789, 936373570430169300, 14654788984834217850, 230405413840884827160, 3637362857723455772670
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+2*x)^3)/x) -
PARI
a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(2*n-k,n-k).