A022454 Expansion of 1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x)).

1, 23, 352, 4530, 53151, 590373, 6335302, 66471680, 687035701, 7029030723, 71413230252, 722053798830, 7276293638251, 73154751811073, 734297855505202, 7362269063785980, 73757914933860801, 738526673084931423

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (23,-177,505,-350).

Formula

a(n) = (8*10^(n+3)-30*7^(n+3)+27*5^(n+3)-5)/1080. -Yahia Kahloune, May 22 2013

a(0)=1, a(1)=23, a(2)=352, a(3)=4530; for n>3, a(n) = 23*a(n-1) -177*a(n-2) +505*a(n-3) -350*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
LinearRecurrence[{23, -177, 505, -350}, {1, 23, 352, 4530}, 20] (* Harvey P. Dale, Nov 07 2013 *)

Prog

(Magma) I:=[1, 23, 352, 4530]; [n le 4 select I[n] else 23*Self(n-1)-177*Self(n-2)+505*Self(n-3)-350*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-7*x)*(1-10*x))) \\ G. C. Greubel, Feb 28 2018

Crossrefs

Sequence in context: A277833 A022469 A028030 * A142617 A025949 A025969

Adjacent sequences: A022451 A022452 A022453 * A022455 A022456 A022457

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved