A391832 a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^k * binomial(2*k+2,2*n-2*k+1).

1, 6, 30, 160, 824, 4112, 20240, 98432, 473648, 2260000, 10707872, 50428928, 236267264, 1101967872, 5119345152, 23699419136, 109371557120, 503331831296, 2310505584128, 10581929451520, 48363392444416, 220617599430656, 1004622677749760, 4567358720147456, 20733836929429504

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-16,16,-72,32,-64,64,-16).

Formula

G.f.: (1-2*x-2*x^2) / ((1-2*x-2*x^2)^2 - 16*x^3)^2.

a(n) = 8*a(n-1) - 16*a(n-2) + 16*a(n-3) - 72*a(n-4) + 32*a(n-5) - 64*a(n-6) + 64*a(n-7) - 16*a(n-8).

Mathematica

CoefficientList[Series[(1-2*x-2*x^2)/((1-2*x-2*x^2)^2-16*x^3)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1-2*x-2*x^2)/((1-2*x-2*x^2)^2-16*x^3)^2)
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-2*x-2*x^2) / ((1-2*x-2*x^2)^2 - 16*x^3)^2); // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A391829, A391835.

Sequence in context: A152224 A238769 A280474 * A208790 A026112 A038155

Adjacent sequences: A391829 A391830 A391831 * A391833 A391834 A391835

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2025

Status

approved