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Cf. A000040.
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a(n) = (k^k + k!) / (k*(k + 1), ), where k = prime(n) - 1.
1, 1, 14, 1128, 90942080, 57157560576, 67818988957718528, 115047995548743401472, 674758653138775267142795264, 40819609745761407890621234130376982528, 221388314080552960064314183934017536000000, 79870389582370042643423622863118514819531536385179648
Andrew Howroyd, <a href="/A178989/b178989.txt">Table of n, a(n) for n = 1..50</a>
(PARI) a(n)={my(k=prime(n)-1); (k^k + k!) / (k*(k + 1))} \\ Andrew Howroyd, Apr 13 2021
Terms a(11) and beyond from Andrew Howroyd, Apr 13 2021
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f[n_] := Block[{k = Prime@ n - 1}, (k^k + k!)/(k (k + 1))]; Array[f, 10] (* _Robert G. Wilson_ v, _, Jan 05 2011 *)
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f[n_] := Block[{k = Prime@ n - 1}, (k^k + k!)/(k (k + 1))]; Array[f, 10] (* Robert G. Wilson, v, Jan 05 2011 *)
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f[n_] := Block[{k = Prime@ n - 1}, (k^k + k!)/(k (k + 1))]; Array[f, 10] (* From _Robert G. Wilson, _, Jan 05 2011 *)