A367592 - OEIS

A367592

Expansion of 1/((1-x) * (1-4*x)^3).

1, 13, 109, 749, 4589, 26093, 140781, 730605, 3679725, 18097645, 87303661, 414459373, 1941186029, 8987616749, 41199871469, 187228759533, 844358755821, 3782116386285, 16838816966125, 74563177424365, 328550363440621, 1441256130749933, 6296699479008749

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (13,-60,112,-64).

FORMULA

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

a(n) = ((9*n^2+21*n+14) * 4^(n+1) - 2)/54.

a(n) = 13*a(n-1) - 60*a(n-2) + 112*a(n-3) - 64*a(n-4). - Wesley Ivan Hurt, Aug 04 2025

E.g.f.: (1/27)*exp(x)*((288*x^2 + 240*x + 28)*exp(3*x) - 1). - Enrique Navarrete, Dec 16 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x)*(1 - 4*x)^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 04 2025 *)

PROG

(PARI) a(n) = ((9*n^2+21*n+14)*4^(n+1)-2)/54;

CROSSREFS

Partial sums of A038845.

Cf. A055580, A367591.

Sequence in context: A002648 A055840 A243417 * A163845 A380001 A075143

Adjacent sequences: A367589 A367590 A367591 * A367593 A367594 A367595

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Nov 24 2023

STATUS

approved