A025958 Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-6*x)).

1, 17, 185, 1645, 13041, 96117, 674185, 4565165, 30122081, 194911717, 1242462585, 7828123485, 48869031121, 302849847317, 1865814241385, 11440608686605, 69880858180161, 425505538990917, 2584272622186585, 15662382429614525, 94760227082369201, 572499821108550517

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17,-104,268,-240).

Formula

a(n) = -2^n/3+16*4^n-125*5^n/3+27*6^n. - R. J. Mathar, Jun 20 2013

a(0)=1, a(1)=17, a(2)=185, a(3)=1645, a(n) = 17*a(n-1)-104*a(n-2)+268*a(n-3)-240*a(n-4). - Harvey P. Dale, Oct 10 2015

a(n) = (4^(n+1)-2^(n+1))/2 + 11*a(n-1) - 30*a(n-2). - Vincenzo Librandi, May 30 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-4*x)*(1-5*x)*(1-6*x)), {x, 0, 30}], x] (* Harvey P. Dale, Oct 10 2015 *)
(* Alternative: *)
LinearRecurrence[{17, -104, 268, -240}, {1, 17, 185, 1645}, 30] (* Harvey P. Dale, Oct 10 2015 *)
(* Alternative: *)
a[0]=1; a[1]=17; Do[a[n]=(4^(n+1)-2^(n+1))/2+11*a[n-1]-30*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, May 30 2026 *)

Prog

(Magma) I:=[1, 17]; [n le 2 select I[n] else (4^n-2^n)/2+11*Self(n-1)-30*Self(n-2): n in [1..22]]; // Vincenzo Librandi, May 30 2026

Crossrefs

Sequence in context: A181401 A243419 A270497 * A199674 A369332 A022741

Adjacent sequences: A025955 A025956 A025957 * A025959 A025960 A025961

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved