A079303 a(n) = ((p-1)!/(2*p^2)) * Sum_{j=1..p-1} 1/j where p is the n-th prime.

1, 18, 43920, 4397760, 122377651200, 30993058252800, 3921055557027840000, 711860093387348628602880000, 551343268152723132127641600000, 567168796017902020698219516788736000000, 1038348796996458761952900456044235325440000000

Offset

3,2

Comments

Always an integer.

Links

Amiram Eldar, Table of n, a(n) for n = 3..87

Formula

a(n) = A000254(A000040(n)-1)/(2*A000040(n)^2).

Mathematica

a[n_] := Module[{p = Prime[n]}, HarmonicNumber[p - 1]*(p - 1)!/(2*p^2)]; Array[a, 10, 3] (* Amiram Eldar, Apr 20 2025 *)

Prog

(PARI) a(n) = my(p=prime(n)); (p-1)!/(2*p^2) * sum(j=1, p-1, 1/j); \\ Michel Marcus, Apr 21 2025

Crossrefs

Cf. A000040, A000254.

Sequence in context: A255406 A123401 A201494 * A159445 A146548 A051591

Adjacent sequences: A079300 A079301 A079302 * A079304 A079305 A079306

Keyword

nonn

Author

Benoit Cloitre, Feb 09 2003

Status

approved