A025467 Expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)*(1-8*x)).

1, 17, 191, 1813, 15855, 132909, 1089607, 8828501, 71093759, 570671101, 4573228023, 36617788389, 293071750063, 2345096538893, 18762876780839, 150111475106677, 1200925773302367, 9607542463373085, 76860885976538455, 614889276376258565, 4919122975724128271, 39353018896026130477

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17,-98,232,-192).

Formula

a(n) = (8^(n+3)-15*4^(n+3)+24*3^(n+3)-10*2^(n+3))/120. - Yahia Kahloune, May 27 2013

a(n) = 3^n-2^n+12*a(n-1)-32*a(n-2). - Vincenzo Librandi, Apr 14 2026

E.g.f.: exp(2*x)*(64*exp(6*x) - 120*exp(2*x) + 81*exp(x) - 10)/15. - Stefano Spezia, Apr 15 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-4x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {17, -98, 232, -192}, {1, 17, 191, 1813}, 30] (* Harvey P. Dale, Jan 31 2023 *)
a[1]=1; a[2]=17; a[n_]:=a[n]=3^n-2^n+12 a[n-1]-32 a[n-2]; Table[a[n], {n, 1, 20}] (* Vincenzo Librandi, Apr 14 2026 *)

Prog

(Magma) I:=[1, 17]; [n le 2 select I[n] else 3^n - 2^n + 12*Self(n-1)-32*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 14 2026

Crossrefs

Sequence in context: A211848 A021754 A141993 * A322122 A210340 A021494

Adjacent sequences: A025464 A025465 A025466 * A025468 A025469 A025470

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 14 2026

Status

approved