A392643 Expansion of 1 / sqrt((1-x)^6 - 4*x^3).

1, 3, 6, 12, 33, 111, 364, 1116, 3339, 10161, 31716, 100206, 316761, 999711, 3158964, 10015848, 31861935, 101581353, 324310822, 1036644708, 3317810325, 10632401247, 34112959080, 109559248392, 352184126953, 1133054637687, 3648128603184, 11754538300422, 37899550584441

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,k) * binomial(n+3*k+2,n-3*k).

Mathematica

Table[Sum[Binomial[2*k, k]*Binomial[n+3*k+2, n-3*k], {k, 0, Floor[n/3]}], {n, 0, 35}] (* Vincenzo Librandi, Jan 19 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x)^6-4*x^3))
(Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!1 / Sqrt((1-x)^6 - 4*x^3)); // Vincenzo Librandi, Jan 19 2026

Crossrefs

Cf. A098479, A392640.

Sequence in context: A066710 A033648 A102972 * A075209 A075207 A208131

Adjacent sequences: A392640 A392641 A392642 * A392644 A392645 A392646

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2026

Status

approved