

A067626


sqrt((1cos(x))/2) = sum(n>=0, (1)^n * x^(2*n+1) / a(n) ).


1



2, 48, 3840, 645120, 185794560, 81749606400, 51011754393600, 42849873690624000, 46620662575398912000, 63777066403145711616000, 107145471557284795514880000, 216862434431944426122117120000
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OFFSET

0,1


COMMENTS

a(n) equals the absolute value of the imaginary part of the determinant of the (4n+2) X (4n+2) matrix with i's along the superdiagonal (where i is the imaginary unit) and 2, 3, 4, ..., 4n+2 along the subdiagonal, and 0's everywhere else (see Mathematica code below).  John M. Campbell, Jun 04 2011


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Eric Weisstein's World of Mathematics, RiemannSiegel Functions


FORMULA

a(n)=A000165(2n+2) where A000165(k) are the double factorial numbers 2^k*k!=(2k)!!.


MAPLE

for n from 0 to 30 by 2 do printf(`%d, `, 2^(n+1)*(n+1)!) od:


MATHEMATICA

Table[Abs[Im[Det[Array[KroneckerDelta[#1 + 1, #2]*I &, {4*n + 2, 4*n + 2}] + Array[KroneckerDelta[#1  1, #2]*#1 &, {4*n + 2, 4*n + 2}]]]], {n, 0, 20}] (* From John M. Campbell, Jun 04 2011 *)
Table[2^(n+1) (n+1)!, {n, 0, 30, 2}] (* Harvey P. Dale, Feb 06 2014 *)


PROG

(MAGMA) [2^(n+1)*Factorial(n+1): n in [0..30 by 2]]; // Vincenzo Librandi, Feb 07 2014


CROSSREFS

Cf. A000165.
Sequence in context: A186416 A210723 A087085 * A053071 A238838 A002820
Adjacent sequences: A067623 A067624 A067625 * A067627 A067628 A067629


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Feb 02 2002


EXTENSIONS

More terms and Maple code from James A. Sellers, Feb 11 2002


STATUS

approved



