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A168467 a(n) = Product_{k=0..n} ((2k+2)(2k+3))^(n-k). 8
1, 6, 720, 3628800, 1316818944000, 52563198423859200000, 327312129899898454671360000000, 428017682605583614976547335700480000000000, 152240508705590071980086429193304853792686080000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform of A000698(n+1).

The sequence 1,1,6,720,... with general term Product{k=0..n, ((2k+1)(2k+0^k))^(n-k)} is the Hankel transform of A112934. - Paul Barry, Dec 04 2009

a(n) = Product_{k=1..n} (2*k+1)!. - Vladimir Reshetnikov, Sep 06 2016

LINKS

Table of n, a(n) for n=0..8.

FORMULA

G.f.: Q(0)/(2*x) -1/x, where Q(k) = 1  + 1/(1 -(2*k+1)!*x/((2*k+1)!*x + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 17 2013

a(n) ~ A^(-1/2) * 2^(n^2 + 3*n + 53/24) * exp((-3/2)*n^2 + (-5/2)*n + 1/24) * n^(n^2 + (5/2)*n + 35/24) * Pi^((n+1)/2), where A = A074962 is the Glaisher-Kinkelin constant. - Vladimir Reshetnikov, Sep 06 2016

a(n) = A000178(2*n + 1) / A098694(n). - Vaclav Kotesovec, Oct 28 2017

MATHEMATICA

Table[2^(n^2 + 2*n + 23/24) Glaisher^(3/2) Pi^(-n/2 - 3/4) BarnesG[n + 2] BarnesG[n + 5/2]/E^(1/8), {n, 0, 10}] (* Vladimir Reshetnikov, Sep 06 2016 *)

CROSSREFS

Sequence in context: A002204 A052295 A169668 * A080369 A036981 A202080

Adjacent sequences:  A168464 A168465 A168466 * A168468 A168469 A168470

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 26 2009

STATUS

approved

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Last modified February 22 23:32 EST 2018. Contains 299472 sequences. (Running on oeis4.)