A381915 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A002293.
1, 3, 18, 145, 1378, 14515, 163700, 1936414, 23716654, 298216851, 3827542585, 49938733635, 660366743580, 8830549084588, 119205253249287, 1622258295003714, 22232669093660250, 306569446979862205, 4250285556933578693, 59210418891925845529, 828417259759216617257
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(3*n-k+1, n-k)/(n+4*k+1));
Formula
G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x*A(x))^2.
a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(3*n-k+1,n-k)/(n+4*k+1).