A025938 Expansion of 1/((1-2*x)*(1-3*x)*(1-6*x)*(1-8*x)).

1, 19, 237, 2471, 23429, 210063, 1818349, 15380167, 128060757, 1054660607, 8618507261, 70035919863, 566816115685, 4573706232751, 36824728021773, 296008336113959, 2376529889559413, 19063018707520095, 152808828368166685, 1224298702679104855, 9805358086293723141, 78508675510891956239

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-124,324,-288).

Formula

a(n) = (2*8^(n+3)-5*6^(n+3)+8*3^(n+3)-5*2^(n+3))/120. - Yahia Kahloune, May 24 2013

a(n) = 3^(n+1)-2^(n+1)+14*a(n-1)-48*a(n-2). - Vincenzo Librandi, Apr 27 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-6x)(1-8x)), {x, 0, 20}], x] (* Harvey P. Dale, Apr 05 2019 *)
(* Alternative: *)
a[0]=1; a[1]=19; a[n_]:=a[n]=3^(n+1)-2^(n+1)+14a[n-1]-48 a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, Apr 27 2026 *)

Prog

(Magma) I:=[1, 19]; [n le 2 select I[n] else 3^n - 2^n + 14*Self(n-1)-48*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 27 2026

Crossrefs

Sequence in context: A152494 A171158 A022033 * A229026 A114757 A142615

Adjacent sequences: A025935 A025936 A025937 * A025939 A025940 A025941

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 27 2026

Status

approved