A392644 Expansion of 1 / ((1-x)^6 - 9*x)^(1/3).

1, 5, 45, 490, 5720, 69477, 865798, 10983770, 141191010, 1833394015, 23998524098, 316182713994, 4188231151213, 55730336729180, 744444532476735, 9977530765306354, 134115304302092618, 1807365910946533092, 24411819111522215806, 330395902080210072950, 4479813492141045978495

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Formula

a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n+5*k+1,n-k).

a(n) = (1 + n)*hypergeom([(2+n)/5, (3+n)/5, (4+n)/5, 1+n/5, (6+n)/5, -n], [1/2, 2/3, 5/6, 1, 7/6], -5^5/72^2). - Stefano Spezia, Jan 18 2026

Mathematica

CoefficientList[Series[1/((1-x)^6-9*x)^(1/3), {x, 0, 25}], x] (* Vincenzo Librandi, Jan 19 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)^6-9*x)^(1/3))
(Magma) R<x> := PowerSeriesRing(Rationals(), 26); f := 1/((1 - x)^6 - 9*x)^(1/3); [ Coefficient(f, i) : i in [0..25] ]; // Vincenzo Librandi, Jan 19 2026

Crossrefs

Cf. A376802, A392645.

Sequence in context: A191095 A202825 A195188 * A232730 A151831 A233834

Adjacent sequences: A392641 A392642 A392643 * A392645 A392646 A392647

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2026

Status

approved