A025927 Expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)*(1-10*x)).

1, 19, 245, 2735, 28701, 293079, 2957125, 29682895, 297294701, 2974868039, 29756539605, 297597360255, 2976103045501, 29761552993399, 297617634403685, 2976184804896815, 29761882021417101, 297618956491125159, 2976190111180805365, 29761903300372004575

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..950

Index entries for linear recurrences with constant coefficients, signature (19,-116,284,-240).

Formula

a(n) = 19*a(n-1) - 116*a(n-2) + 284*a(n-3) - 240*a(n-4), with a(0)=1, a(1)=19, a(2)=245, a(3)=2735. - Harvey P. Dale, Oct 18 2011

a(n) = (10^(n+3) - 7*4^(n+4) + 16*3^(n+4) - 21*2^(n+3))/336. - Yahia Kahloune, May 19 2013

a(n) = 3^(n+1) - 2^(n+1) + 14*a(n-1) - 40*a(n-2). - Vincenzo Librandi, Apr 15 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-4x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{19, -116, 284, -240}, {1, 19, 245, 2735}, 31] (* Harvey P. Dale, Oct 18 2011 *)
a[0]=1; a[1]=19; a[n_]:=a[n]=3^(n+1)-2^(n+1)+14 a[n-1]-40 a[n-2]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Apr 15 2026 *)

Prog

(PARI) Vec((-4560*x^3 + 5156*x^2 - 1920*x + 245)/(240*x^4 - 284*x^3 + 116*x^2 - 19*x + 1)+O(x^25)) \\ Charles R Greathouse IV, May 20 2013
(Magma) I:=[1, 19]; [n le 2 select I[n] else 3^n - 2^n + 14*Self(n-1)-40*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 15 2026

Crossrefs

Sequence in context: A019783 A021504 A019512 * A224180 A318194 A019443

Adjacent sequences: A025924 A025925 A025926 * A025928 A025929 A025930

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 15 2026

Status

approved