A391890 a(n) = Sum_{k=0..n} (k+1) * binomial(2*k+1,2*n-2*k+1).

1, 6, 17, 58, 188, 570, 1715, 5074, 14787, 42676, 122104, 346804, 979013, 2749150, 7684437, 21393326, 59346996, 164112814, 452535543, 1244660906, 3415404295, 9352256360, 25559520752, 69730069352, 189923821833, 516517036214, 1402761072409, 3804691897890, 10306957986220

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-2,0,-11,0,-2,4,-1).

Formula

G.f.: ((1-x-x^2)^2 + 4*x - 4*x^2) / ((1-x-x^2)^2 - 4*x^3)^2.

a(n) = 4*a(n-1) - 2*a(n-2) - 11*a(n-4) - 2*a(n-6) + 4*a(n-7) - a(n-8).

Mathematica

CoefficientList[Series[((1-x-x^2)^2+4*x-4*x^2)/((1-x-x^2)^2-4*x^3)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Jan 01 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(((1-x-x^2)^2+4*x-4*x^2)/((1-x-x^2)^2-4*x^3)^2)
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2)^2 + 4*x - 4*x^2) / ((1-x-x^2)^2 - 4*x^3)^2); // Vincenzo Librandi, Jan 01 2026

Crossrefs

Cf. A381421, A391829, A391891.

Sequence in context: A088016 A010330 A109311 * A151350 A195741 A006758

Adjacent sequences: A391887 A391888 A391889 * A391891 A391892 A391893

Keyword

nonn

Author

Seiichi Manyama, Dec 22 2025

Status

approved