A372038 G.f. A(x) satisfies A(x) = ( 1 + 9*x*(1 + x)*A(x) )^(1/3).
1, 3, 3, -9, 0, 81, -171, -621, 3672, 324, -54918, 125145, 563922, -3381345, -1013553, 59036607, -128956455, -693917604, 3979050642, 2186515944, -76048363647, 153593093106, 978492895848, -5278059507771, -4343581909296, 107892778958370, -197193416230692
Offset: 0
Keywords
Crossrefs
Cf. A372036.
Programs
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PARI
a(n) = sum(k=0, n, 9^k*binomial(k/3+1/3, k)*binomial(k, n-k)/(k+1));
Formula
a(n) = Sum_{k=0..n} 9^k * binomial(k/3+1/3,k) * binomial(k,n-k)/(k+1).