A072118 - OEIS

A072118

a(n) = (2*n)!/core(n!)^2/(n+1) where core(x) is the squarefree part of x.

1, 2, 5, 224, 672, 2737152, 8895744, 474439680, 130660687872, 4513732853760000, 15798064988160000, 894413525483520000, 3194334019584000000, 27610545531676262400000, 8107146431738442547200000, 7569213421444268241715200000, 27753782545295650219622400000

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OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..251

MATHEMATICA

f[p_, e_] := p^Mod[e, 2]; a[1] = 1; a[n_] := (2*n)! / ((Times @@ f @@@ FactorInteger[n!])^2 * (n+1)); Array[a, 17] (* Amiram Eldar, May 01 2025 *)

PROG

(PARI) a(n) = (2*n)!/core(n!)^2/(n+1);

CROSSREFS

Cf. A007913, A055204.

Sequence in context: A084297 A041873 A382350 * A249180 A135724 A137068