A390687 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-2*k,n-2*k).

1, 4, 27, 210, 1730, 14704, 127470, 1120262, 9944676, 88961008, 800658947, 7241596046, 65764261576, 599284477328, 5477020329872, 50182223592510, 460796527028636, 4239427396585840, 39070459427293260, 360622779428966656, 3333138696913131830, 30845466968858253248

Offset

0,2

Links

Seiichi Manyama, 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+2,n-k).

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k, n-2*k));

Crossrefs

Cf. A176332, A390686.

Sequence in context: A386959 A059391 A371786 * A190738 A361717 A275607

Adjacent sequences: A390684 A390685 A390686 * A390688 A390689 A390690

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved