A378555 a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+k-1,k) * binomial(k/3,n-k).
1, 1, 9, 19, 305, 156, 13233, -23988, 688113, -2863070, 41085704, -246536784, 2696513885, -19410931916, 187672944300, -1481383572516, 13522625165601, -111877103550195, 994511499413664, -8430550720540365, 74061353032540020, -636000265949289978
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[1/(1 - x*(1 + 9*x)^(1/3))^n,{x,0,n}]; Array[a,22,0] (* Stefano Spezia, Nov 30 2024 *) -
PARI
a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k-1, k)*binomial(k/3, n-k));
Formula
a(n) = [x^n] 1/(1 - x*(1 + 9*x)^(1/3))^n.