A390849 a(n) = Sum_{k=0..n} (k+1) * 2^k * 3^(n-k) * binomial(2*k,2*(n-k)).

1, 4, 24, 248, 1628, 11232, 77632, 513088, 3372816, 21936320, 141137024, 901877376, 5725796800, 36148870144, 227148097536, 1421370361856, 8861474185472, 55066373329920, 341189723846656, 2108443851544576, 12998518366460928, 79962302352957440, 490928459988451328

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,0,-16,-328,-96,0,1728,-1296).

Formula

G.f.: ((1-2*x-6*x^2)^2 + 48*x^3) / ((1-2*x-6*x^2)^2 - 48*x^3)^2.

a(n) = 8*a(n-1) - 16*a(n-3) - 328*a(n-4) - 96*a(n-5) + 1728*a(n-7) - 1296*a(n-8).

Mathematica

CoefficientList[Series[((1-2*x-6*x^2)^2+48*x^3)/((1-2*x-6*x^2)^2-48*x^3)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)

Prog

(PARI) my(A=2, B=3, C=4*A^2*B, N=2, M=30, x='x+O('x^M), X=1-A*x-A*B*x^2, Y=3); Vec(sum(k=0, N\2, C^k*binomial(N, 2*k)*X^(N-2*k)*x^(Y*k))/(X^2-C*x^Y)^N)
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! ((1-2*x-6*x^2)^2 + 48*x^3) / ((1-2*x-6*x^2)^2 - 48*x^3)^2); // Vincenzo Librandi, Jan 03 2026

Crossrefs

Cf. A108486, A391779.

Cf. A381421, A390781.

Sequence in context: A126391 A006088 A325963 * A141013 A330469 A227467

Adjacent sequences: A390846 A390847 A390848 * A390850 A390851 A390852

Keyword

nonn

Author

Seiichi Manyama, Dec 19 2025

Status

approved