A136411 a(n) = Product_{k=1..n} (2*k-1)^(2*n-2*k+1).

1, 3, 135, 212625, 21097715625, 207248662456171875, 291128066470548703880859375, 79746389028864195813528714933837890625, 5570294521107277357810167397301815834831695556640625

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..29

Formula

a(n) = A107254(n) / 2^(n*(n - 1)).

a(n) = sf(2*n-1) / (2^(n*(n-1)) * sf(n-1)^2), n >= 1, where sf(n) = BarnesG(n + 2) is the superfactorial defined in A000178. - Robert Coquereaux, Apr 02 2013

a(n) ~ A * 2^(n^2 + n - 1/12) * n^(n^2 + 1/12) / exp(3*n^2/2 + 1/12), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015

Mathematica

Table[Product[(2*k - 1)^(2*n - 2*k + 1), {k, 1, n}], {n, 1, 10}] (* Stefan Steinerberger, May 18 2008 *)
sf[n_] := BarnesG[n + 2]; a[n_] := sf[2 n - 1]/(2^(n (n - 1)) sf[n - 1]^2); Table[a[n], {n, 1, 10}]  (* Robert Coquereaux, Apr 02 2013 *)

Prog

(PARI) a(n) = prod(k=1, n, (2*k-1)^(2*n-2*k+1)) \\ Anders Hellström, Sep 16 2015
(Magma) [(&*[(2*k-1)^(2*n-2*k+1): k in [1..n]]): n in [1..10]]; // G. C. Greubel, Oct 14 2018

Crossrefs

Cf. A136807, A087315, A000178, A055209.

Sequence in context: A065973 A110973 A361195 * A193136 A037120 A082923

Adjacent sequences: A136408 A136409 A136410 * A136412 A136413 A136414

Keyword

easy,nonn

Author

Ctibor O. Zizka, Mar 31 2008

Extensions

More terms from Stefan Steinerberger, May 18 2008

Status

approved