A392579 Expansion of 1 / ((1-x)^4 - x)^2.

1, 10, 63, 328, 1551, 6936, 29915, 125784, 518994, 2110412, 8482705, 33775188, 133430068, 523642612, 2043423819, 7935173028, 30683010755, 118196391378, 453794172258, 1737066730472, 6631442585508, 25254895540622, 95967876337585, 363942611155956, 1377653583826008

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-37,68,-78,58,-28,8,-1).

Formula

a(n) = Sum_{k=0..n} (k+1) * binomial(n+3*k+7,n-k).

a(n) = 10*a(n-1) - 37*a(n-2) + 68*a(n-3) - 78*a(n-4) + 58*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

Mathematica

CoefficientList[Series[1/((1-x)^4-x)^2, {x, 0, 25}], x] (* Vincenzo Librandi, Jan 18 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)^4-x)^2)
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! 1 / ((1-x)^4 - x)^2); // Vincenzo Librandi, Jan 18 2026

Crossrefs

Cf. A055991.

Sequence in context: A055368 A278802 A077616 * A145885 A093953 A298067

Adjacent sequences: A392576 A392577 A392578 * A392580 A392581 A392582

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 17 2026

Status

approved