A025932 Expansion of 1/((1-2*x)*(1-3*x)*(1-5*x)*(1-8*x)).

1, 18, 213, 2114, 19173, 165354, 1384741, 11393778, 92748645, 750039290, 6040740069, 48528576642, 389243479717, 3119026937226, 24977625311397, 199948094540306, 1600220345577189, 12804941098049562, 102455421613293925, 819722840536574370, 6558180072901965861, 52467427357639446698

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-111,278,-240).

Formula

From Vincenzo Librandi, Mar 19 2011: (Start)

a(n) = 18*a(n-1) - 111*a(n-2) + 278*a(n-3) - 240*a(n-4), n >= 4.

a(n) = 13*a(n-1) - 40*a(n-2) + 3^(n+1) - 2^(n+1), n >= 2. (End)

a(n) = 4*8^(n+2)/45 - 2^(n+2)/9 - 5^(n+3)/18 + 3^(n+3)/10. - R. J. Mathar, Mar 19 2011

Mathematica

a[0]=1; a[1]=18; a[n_]:=a[n]=3^(n+1)-2^(n+1)+13a[n-1]-40 a[n-2]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Apr 19 2026 *)

Prog

(Magma) I:=[1, 18]; [n le 2 select I[n] else 3^n-2^n+13*Self(n-1)-40*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 19 2026

Crossrefs

Sequence in context: A004323 A025937 A021804 * A260569 A125430 A021764

Adjacent sequences: A025929 A025930 A025931 * A025933 A025934 A025935

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 19 2026

Status

approved