A368892 a(n) = Sum_{k=0..floor(n/3)} n^(n-3*k) * binomial(n-2*k,k).
1, 1, 4, 28, 264, 3200, 47521, 835569, 16974208, 391147867, 10080150040, 287244283821, 8967781893889, 304393809948904, 11160668048222588, 439582708115133751, 18509867068477014112, 829768603643818659302, 39454459640462073466945
Offset: 0
Programs
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Mathematica
Join[{1}, Table[n^n * HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2 - n/2, -n/2}, -27/(4*n^3)], {n, 1, 20}]] (* Vaclav Kotesovec, Jan 09 2024 *) -
PARI
a(n) = sum(k=0, n\3, n^(n-3*k)*binomial(n-2*k, k));
Formula
a(n) = [x^n] 1/(1 - n*x - x^3).
a(n) ~ n^n. - Vaclav Kotesovec, Jan 09 2024