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%I #10 Jan 09 2024 08:45:16
%S 1,1,4,28,264,3200,47521,835569,16974208,391147867,10080150040,
%T 287244283821,8967781893889,304393809948904,11160668048222588,
%U 439582708115133751,18509867068477014112,829768603643818659302,39454459640462073466945
%N a(n) = Sum_{k=0..floor(n/3)} n^(n-3*k) * binomial(n-2*k,k).
%F a(n) = [x^n] 1/(1 - n*x - x^3).
%F a(n) ~ n^n. - _Vaclav Kotesovec_, Jan 09 2024
%t 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 *)
%o (PARI) a(n) = sum(k=0, n\3, n^(n-3*k)*binomial(n-2*k, k));
%Y Cf. A368891, A368893.
%Y Cf. A117716, A084845.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Jan 09 2024
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