A023951 Expansion of g.f. 1/((1-x)*(1-6*x)*(1-7*x)*(1-10*x)).

1, 24, 381, 5056, 60837, 689640, 7521277, 79922832, 834214293, 8599137976, 87862904493, 892165074528, 9019015091269, 90887374167432, 913848341454429, 9173869834986544, 91989788624850165, 921675830164728408, 9229325781008873485, 92381961397307873280, 924444926473740777381

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-195,592,-420).

Formula

a(n) = (5*10^(n+3) - 30*7^(n+3) + 27*6^(n+3) - 2)/540. - Yahia Kahloune, Jun 29 2013

a(n) = 24*a(n-1) -195*a(n-2) +592*a(n-3) -420*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 6 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)
LinearRecurrence[{24, -195, 592, -420}, {1, 24, 381, 5056}, 30] (* Harvey P. Dale, Apr 29 2025 *)

Prog

(Magma) I:=[1, 24, 381, 5056]; [n le 4 select I[n] else 24*Self(n-1)-195*Self(n-2)+592*Self(n-3)-420*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 12 2013
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-7*x)*(1-10*x)))); // Vincenzo Librandi, Jul 12 2013

Crossrefs

Sequence in context: A023954 A028036 A025977 * A025990 A022565 A025974

Adjacent sequences: A023948 A023949 A023950 * A023952 A023953 A023954

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved