A028178 Expansion of 1/((1-5x)(1-6x)(1-10x)(1-12x)).

1, 33, 697, 12045, 186001, 2677653, 36790057, 489351885, 6359059201, 81227776773, 1024237953817, 12787834412925, 158435642617201, 1951116268675893, 23912720464211977, 291948566493573165, 3553358170873164001, 43140149525240231013, 522680899336759084537

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (33,-392,1980,-3600).

Formula

a(n) = (4*12^(n+2)-7*10^(n+2)+7*6^(n+2)-4*5^(n+2))/28. [Yahia Kahloune, Jun 04 2013]

G.f.: 1/((1-5x)(1-6x)(1-10x)(1-12x)).

a(n) = 33*a(n-1)-392*a(n-2)+1980*a(n-3)-3600*a(n-4). - Wesley Ivan Hurt, Mar 10 2015

Maple

A028178:=n->(4*12^(n+2)-7*10^(n+2)+7*6^(n+2)-4*5^(n+2))/28: seq(A028178(n), n=0..20); # Wesley Ivan Hurt, Mar 10 2015

Mathematica

CoefficientList[Series[1/((1 - 5 x) (1 - 6 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x]
LinearRecurrence[{33, -392, 1980, -3600}, {1, 33, 697, 12045}, 20] (* Harvey P. Dale, Jul 26 2020 *)

Prog

(Magma) [(4*12^(n+2)-7*10^(n+2)+7*6^(n+2)-4*5^(n+2))/28 : n in [0..20]]; // Wesley Ivan Hurt, Mar 10 2015

Crossrefs

Sequence in context: A028186 A028158 A028157 * A028153 A028105 A028103

Adjacent sequences: A028175 A028176 A028177 * A028179 A028180 A028181

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved