A271421 a(n) = fibonorial(3*n)/(fibonorial(2*n+1)*fibonorial(n+1)), where fibonorial(n) = A003266(n).

1, 4, 119, 23496, 32149806, 300214157831, 19246160432331107, 8451529006578585976752, 25443734373070679510011112460, 524973397889459587964008354031908560, 74243674067972394056586805754940632245000310, 71965837912588688126721254257169744333502564695515911

Offset: 1

Author

Vladimir Reshetnikov, May 21 2016

Keywords

• nonn
• easy

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.5.

Links

• Simon Plouffe, Fibonacci factorials.
• Eric Weisstein's World of Mathematics, Fibonorial, Fibonacci Factorial Constant.

Crossrefs

Cf. A003266, A003267, A003268, A062073, A003150, A000045.

Programs

Mathematica

Table[Fibonorial[3 n]/(Fibonorial[2 n + 1] Fibonorial[n + 1]), {n, 1, 30}] (* The sequence itself *)
QPochhammer[-1/GoldenRatio^2] (* The Fibonacci factorial constant C in the asymptotic expansion *)

Formula

a(n) ~ 5*phi^(2*n^2 - 3*n - 2)/C where phi = (1+sqrt(5))/2, and C = (-1/phi^2; -1/phi^2)_inf is the Fibonacci factorial constant whose decimal expansion is given in A062073.