A025980 Expansion of 1/((1-2*x)*(1-4*x)*(1-9*x)*(1-10*x)).

1, 25, 413, 5717, 71949, 854517, 9768541, 108728389, 1186801517, 12764197589, 135709713789, 1429715165541, 14950747454605, 155389970948341, 1606842713958557, 16544916327312773, 169737574552541613, 1735971481399748373, 17707076574305165245, 180197022135576075685

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (25,-212,692,-720).

Formula

a(n) = -2^n/14 +16*4^n/15-729*9^n/35+125*10^n/6. - R. J. Mathar, Jun 20 2013

a(n) = (4^(n+1)-2^(n+1))/2+19*a(n-1)-90*a(n-2). - Vincenzo Librandi, Jul 01 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-9x)(1-10x)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 06 2020 *)
(* Alternative: *)
a[0]=1; a[1]=25; Do[a[n]=(4^(n+1)-2^(n+1))/2+19*a[n-1]-90*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 19}] (* Vincenzo Librandi, Jul 01 2026 *)

Prog

(Magma) I:=[1, 25]; [n le 2 select I[n] else (4^n-2^n)/2+19*Self(n-1)-90*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jul 01 2026

Crossrefs

Sequence in context: A028041 A025995 A023955 * A387313 A025978 A028037

Adjacent sequences: A025977 A025978 A025979 * A025981 A025982 A025983

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jul 01 2026

Status

approved