A369509 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2-x)^2 ).
1, 6, 61, 756, 10406, 152880, 2348164, 37250298, 605592377, 10036783746, 168947499695, 2880456168330, 49638925087101, 863251245610368, 15130529347412496, 267011151724625220, 4740245924729076390, 84599747038748783220, 1516992745930706932654
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2-x)^2)/x) -
PARI
a(n) = sum(k=0, n, binomial(2*n+k+1, k)*binomial(5*n+k+3, n-k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(5*n+k+3,n-k).