A392642 Expansion of 1 / sqrt((1-x)^6 - 4*x^2).

1, 3, 8, 28, 111, 441, 1758, 7110, 29101, 120003, 497598, 2073074, 8671473, 36394155, 153183348, 646345300, 2733100395, 11579042025, 49138564920, 208846332468, 888831570633, 3787421110239, 16156612556814, 68991749120934, 294881166562561, 1261442199126447

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[Binomial[2*k, k]*Binomial[n+4*k+2, n-2*k], {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Jan 19 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x)^6-4*x^2))
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R! 1 / Sqrt((1-x)^6 - 4*x^2)); // Vincenzo Librandi, Jan 19 2026

Crossrefs

Cf. A002426, A101500.

Sequence in context: A224271 A135583 A317077 * A009437 A347072 A000776

Adjacent sequences: A392639 A392640 A392641 * A392643 A392644 A392645

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2026

Status

approved