OFFSET
0,1
LINKS
J. L. Jacobsen and P. Zinn-Justin, A Transfer Matrix approach to the Enumeration of Knots, arXiv:math-ph/0102015, 2001-2002.
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
MAPLE
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
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 05 2002
EXTENSIONS
More terms from James A. Sellers, Feb 11 2002
STATUS
approved