A381827 G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108.
1, 2, 10, 69, 562, 5042, 48100, 478547, 4908338, 51522174, 550758208, 5974753990, 65608248500, 727835313461, 8144965594184, 91834891588099, 1042244963201914, 11896871741939462, 136493661712053752, 1573151972820654218, 18205626549920314728, 211468167403628323318
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Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*n-k+1, k)*binomial(4*n-4*k, n-k)/(3*n-k+1));
Formula
a(n) = Sum_{k=0..n} binomial(3*n-k+1,k) * binomial(4*n-4*k,n-k)/(3*n-k+1).