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a(n) = (floor(n/2)+1)^n.

2

`%I #10 Oct 08 2016 12:33:00
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`%S 1,4,8,81,243,4096,16384,390625,1953125,60466176,362797056,
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`%T 13841287201,96889010407,4398046511104,35184372088832,
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`%U 1853020188851841,16677181699666569,1000000000000000000,10000000000000000000,672749994932560009201
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`%N a(n) = (floor(n/2)+1)^n.
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`%C Functions from [n] to [n] with f(i) even or f(i) = 1 for all i.
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`%C Functions from [n] to [n] with f(i) odd or f(i) = n for all i.
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`%t Table[(Floor[n/2] + 1)^n, {n, 1, 20}]
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`%o (PARI) a(n) = (n\2 + 1)^n; \\ _Michel Marcus_, Oct 08 2016
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`%Y Cf. A206344, A276978.
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`%K nonn,easy
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`%O 1,2
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`%A _Olivier GĂ©rard_, Sep 23 2016
`