A067636 Row 1 of table in A067640.

2, 20, 210, 2352, 27720, 339768, 4294290, 55621280, 734959368, 9873696560, 134510127752, 1854385377600, 25828939188000, 362995937665200, 5141806953167250, 73343003232628800, 1052697272275341000, 15194039267330154000, 220410039466873456200

Offset: 0

Author

N. J. A. Sloane, Feb 05 2002

Keywords

• nonn
• easy

Links

• J. L. Jacobsen and P. Zinn-Justin, A Transfer Matrix approach to the Enumeration of Knots, arXiv:math-ph/0102015, 2001-2002.

Crossrefs

Cf. A005568 (row 0), A067637 (row 2), A067638 (row 3), A067639 (row 4).

Programs

Maple

seq((2*n+2)!*(2*n+4)!/(n!*((n+2)!)^2*(n+3)!),n=0..30); # James Sellers, Feb 11 2002; adapted to offset 0 by Georg Fischer, May 29 2021

Mathematica

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 *)

Formula

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

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

a(n) ~ 2^(4*n + 6) / (Pi*n^2). - Vaclav Kotesovec, May 29 2021

Extensions

More terms from James Sellers, Feb 11 2002