A025942 Expansion of 1/((1-2*x)*(1-3*x)*(1-6*x)*(1-12*x)).

1, 23, 361, 4907, 62545, 773171, 9415897, 113824139, 1370909089, 16481083619, 197954225833, 2376538571771, 28524991618033, 342339076723667, 4108303998843769, 49301058498065003, 591621165177427777, 7099504761720178115, 85194361819350143305, 1022334169907935491035, 12268021007360086776721

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,-168,468,-432).

Formula

a(0)=1, a(1)=23, a(2)=361, a(3)=4907, a(n) = 23*a(n-1)-168*a(n-2)+468*a(n-3)-432*a(n-4). - Harvey P. Dale, Oct 20 2012

a(n) = 16*12^n/5-3*6^n-2^n/5+3^n.- R. J. Mathar, Jun 04 2013

a(n) = 3^(n+1)-2^(n+1)+18*a(n-1)-72*a(n-2). - Vincenzo Librandi, May 04 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-6*x)*(1-12*x)), {x, 0, 30}], x] (* Harvey P. Dale, Oct 20 2012 *)
(* Alternative *)
LinearRecurrence[{23, -168, 468, -432}, {1, 23, 361, 4907}, 20] (* Harvey P. Dale, Oct 20 2012 *)
(* Alternative *)
a[0]=1; a[1]=23; a[n_]:=a[n]=3^(n+1)-2^(n+1)+18*a[n-1]-72*a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, May 04 2026 *)

Prog

(PARI) Vec(1/((1-2*x)*(1-3*x)*(1-6*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) I:=[1, 23]; [n le 2 select I[n] else 3^n-2^n+18*Self(n-1)-72*Self(n-2): n in [1..25]]; // Vincenzo Librandi, May 04 2026

Crossrefs

Sequence in context: A021684 A138578 A077515 * A020000 A021664 A202666

Adjacent sequences: A025939 A025940 A025941 * A025943 A025944 A025945

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 04 2026

Status

approved