A025989 Expansion of 1/((1-2*x)*(1-5*x)*(1-6*x)*(1-10*x)).

1, 23, 347, 4375, 50211, 546063, 5750347, 59371895, 605580371, 6130227103, 61765086747, 620509140615, 6222647943331, 62333853156143, 623992946413547, 6243906815856535, 62463186581999091, 624777847926261183, 6248660729728834747, 62491932589229215655, 624951436589656067651

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (23,-182,580,-600).

Formula

a(n) = -2^n/12+25*5^n/3-27*6^n/2+25*10^n/4. - R. J. Mathar, Jun 20 2013

a(n) = (5^(n+1)-2^(n+1))/3+16*a(n-1)-60*a(n-2). - Vincenzo Librandi, Jul 07 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-5x)(1-6x)(1-10x)), {x, 0, 20}], x] (* Harvey P. Dale, Apr 01 2011 *)
(* Alternative: *)
a[0]=1; a[1]=23; Do[a[n]=(5^(n+1)-2^(n+1))/3+16*a[n-1]-60*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Jul 07 2026 *)

Prog

(Magma) I:=[1, 23]; [n le 2 select I[n] else (5^n-2^n)/3+16*Self(n-1)-60*Self(n-2): n in [1..21]]; // Vincenzo Librandi, Jul 07 2026

Crossrefs

Sequence in context: A077309 A042016 A025976 * A125480 A023950 A268465

Adjacent sequences: A025986 A025987 A025988 * A025990 A025991 A025992

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jul 07 2026

Status

approved