A390685 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-2*k-2,n-2*k).

1, 2, 14, 112, 936, 8022, 69920, 616816, 5490860, 49224656, 443782794, 4019371712, 36543625868, 333329554820, 3048897624904, 27954855390752, 256853762314268, 2364400050657240, 21800800394896280, 201309698912840512, 1861373182485257596, 17231521108619924614

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = [x^n] 1/((1+x^2) * (1-x)^(3*n-1)).

a(n) = Sum_{k=0..n} (-2)^k * binomial(4*n+k,n-k).

Mathematica

Table[Sum[(-1)^k*Binomial[4*n-2*k-2, n-2*k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 16 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k-2, n-2*k));
(Magma) [&+[(-1)^k*Binomial(4*n-2*k-2, n-2*k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 16 2025

Crossrefs

Cf. A390683, A390684.

Sequence in context: A359108 A214766 A393178 * A330553 A275649 A199649

Adjacent sequences: A390682 A390683 A390684 * A390686 A390687 A390688

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved