A379174 G.f. A(x) satisfies A(x) = (1 + x*A(x)^3)/(1 - x*A(x))^2.
1, 3, 20, 176, 1772, 19309, 221651, 2640016, 32322122, 404256442, 5142846467, 66341063274, 865723122919, 11408144684248, 151593390664710, 2029025599194394, 27330120599494110, 370183683091079836, 5038997387800717228, 68896081533831380702, 945747379824209853435
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(3*n+3*k+1, n-k)/(n+2*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+2*k+1,k) * binomial(3*n+3*k+1,n-k)/(n+2*k+1).