A025928 Expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)*(1-11*x)).

1, 20, 275, 3310, 37761, 421440, 4662175, 51395570, 565817021, 6225908260, 68492850075, 753453315030, 8288115908281, 91169797529480, 1002869877293975, 11031577111093690, 121347382194479541, 1334821340416229100, 14683035290848073875, 161513390387892763550

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (20,-125,310,-264).

Formula

a(n) = 20*a(n-1)-125*a(n-2)+ 310*a(n-3)- 264*a(n-4), with a(0)=1, a(1)=20, a(2)=275, a(3)=3310. - Harvey P. Dale, May 24 2012

a(n) = (11^(n+3)-9*4^(n+4)+7*3^(n+5)-7*2^(n+5))/504. - Yahia Kahloune, May 20 2013

a(n) = 3^(n+1) - 2^(n+1) + 15*a(n-1) - 44*a(n-2). - Vincenzo Librandi, Apr 17 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-4x)(1-11x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{20, -125, 310, -264}, {1, 20, 275, 3310}, 30] (* Harvey P. Dale, May 24 2012 *)
a[0]=1; a[1]=20; a[n_]:=a[n]=3^(n+1)-2^(n+1)+15 a[n-1]-44 a[n-2]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Apr 17 2026 *)

Prog

(PARI) Vec(1/((1-2*x)*(1-3*x)*(1-4*x)*(1-11*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(Magma) I:=[1, 20]; [n le 2 select I[n] else 3^n - 2^n + 15*Self(n-1)-44*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 17 2026

Crossrefs

Sequence in context: A121117 A278722 A021264 * A004334 A019483 A018056

Adjacent sequences: A025925 A025926 A025927 * A025929 A025930 A025931

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved