A119698 a(n) = n^3*binomial(2*n, n)*Fibonacci(n)^2.

0, 2, 48, 2160, 40320, 787500, 12773376, 198942744, 2905943040, 40973240880, 558886900000, 7437264466632, 96894798594048, 1240510066959800, 15645553270401600, 194802398523000000, 2398428702498447360, 29240457953102773740, 353391128284307097600

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

Sum_{n>=0} a(n)/16^n = (2 + sqrt(2743525 + 5578*sqrt(5)))/(100*sqrt(5)). - Amiram Eldar, May 05 2023

Maple

[seq(combinat:-fibonacci(n)^2*n^3*binomial(2*n, n), n=0..20)];

Mathematica

a[n_] := n^3 * Binomial[2 n, n] * Fibonacci[n]^2; Array[a, 25, 0] (* Amiram Eldar, May 05 2023 *)

Prog

(PARI) a(n) = n^3*binomial(2*n, n)*fibonacci(n)^2; \\ Michel Marcus, Sep 07 2014

Crossrefs

Cf. A000045, A000984.

Sequence in context: A348322 A186284 A119695 * A112103 A367254 A177317

Adjacent sequences: A119695 A119696 A119697 * A119699 A119700 A119701

Keyword

nonn,easy

Author

Zerinvary Lajos, Jun 09 2006

Extensions

Title corrected by Derek Orr, Sep 07 2014

Maple program corrected by Robert Israel, Sep 07 2014

More terms from Michel Marcus, Sep 08 2014

Status

approved