A025967 Expansion of 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-9*x)).

1, 21, 289, 3321, 34705, 343257, 3282913, 30740457, 283960369, 2599944633, 23667405697, 214622461833, 1941330570193, 17530479823449, 158125883415841, 1425244488222249, 12839878208747377, 115635005126816505, 1041171791068580545, 9373287138935906505, 84376032565357455121

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-152,444,-432).

Formula

a(n) = (8*9^(n+3)-35*6^(n+3)+42*4^(n+3)-15*2^(n+3))/840. - Yahia Kahloune, May 24 2013

a(n) = (4^(n+1)-2^(n+1))/2 + 15*a(n-1) - 54*a(n-2). - Vincenzo Librandi, Jun 10 2026

Mathematica

a[0]=1; a[1]=21; Do[a[n]=(4^(n+1)-2^(n+1))/2+15*a[n-1]-54*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, Jun 10 2026 *)

Prog

(Magma) I:=[1, 21]; [n le 2 select I[n] else (4^n-2^n)/2+15*Self(n-1)-54*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 10 2026

Crossrefs

Sequence in context: A316924 A317042 A317696 * A388207 A022452 A183731

Adjacent sequences: A025964 A025965 A025966 * A025968 A025969 A025970

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 10 2026

Status

approved