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A067636 Row 1 of table in A067640. 1

%I

%S 2,20,210,2352,27720,339768,4294290,55621280,734959368,9873696560,

%T 134510127752,1854385377600,25828939188000,362995937665200,

%U 5141806953167250,73343003232628800,1052697272275341000,15194039267330154000,220410039466873456200

%N Row 1 of table in A067640.

%H J. L. Jacobsen and P. Zinn-Justin, <a href="http://arXiv.org/abs/math-ph/0102015">A Transfer Matrix approach to the Enumeration of Knots</a>, arXiv:math-ph/0102015, 2001-2002.

%F a(n) = (2*n+2)!*(2*n+4)!/(n!*((n+2)!)^2*(n+3)!). [adapted to offset 0 by _Georg Fischer_, May 29 2021]

%F D-finite with recurrence: a(0) = 2, n*(n+2)*(n+3)*a(n) - 4*(n+1)*(2*n+1)*(2*n+3)*a(n-1) = 0 for n >= 1. - _Georg Fischer_, May 29 2021

%F a(n) ~ 2^(4*n + 6) / (Pi*n^2). - _Vaclav Kotesovec_, May 29 2021

%p seq((2*n+2)!*(2*n+4)!/(n!*((n+2)!)^2*(n+3)!),n=0..30); # _James A. Sellers_, Feb 11 2002; adapted to offset 0 by _Georg Fischer_, May 29, 2021

%t RecurrenceTable[{n*(n+2)*(n+3)*a[n] - 4*(n+1)*(2*n+1)*(2*n+3)*a[n-1] == 0, a[0]==2},a,{n,0,16}] (* _Georg Fischer_, May 29 2021 *)

%Y Cf. A005568 (row 0), A067638 (row 2), A067639 (row 3).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Feb 05 2002

%E More terms from _James A. Sellers_, Feb 11 2002

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Last modified July 24 17:43 EDT 2021. Contains 346273 sequences. (Running on oeis4.)