A390682 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-2*k-3,n-2*k).

1, 1, 9, 77, 661, 5746, 50523, 448362, 4008533, 36053380, 325870824, 2957523101, 26935038035, 246034329464, 2253137901810, 20680064292992, 190182848146261, 1752060524980444, 16166038630080780, 149370805466634900, 1381899037530298996, 12799247925812071158

Offset

0,3

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-2)).

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

Mathematica

Table[Sum[(-2)^k*Binomial[4*n+k-1, n-k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Nov 18 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k-3, n-2*k));
(Magma) [&+[(-2)^k*Binomial(4*n+k-1, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 18 2025

Crossrefs

Cf. A390680, A390681.

Cf. A371815, A390685, A390687.

Sequence in context: A126631 A190981 A254659 * A397383 A346847 A355372

Adjacent sequences: A390679 A390680 A390681 * A390683 A390684 A390685

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved