A025945 Expansion of 1/((1-2*x)*(1-3*x)*(1-7*x)*(1-10*x)).

1, 22, 323, 4016, 45873, 499386, 5280511, 54817972, 562288925, 5721711710, 57909049419, 583934547768, 5873255438857, 58969928883394, 591360924613847, 5925240739579004, 59333827978882869, 593908224257636838, 5943071855019762595, 59458645840787121280, 594781949452455936161, 5949187931868029290442

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-161,452,-420).

Formula

a(n) = 125*10^n/21-7^(n+3)/60-2^n/5+3^(n+3)/28. - R. J. Mathar, Jun 04 2013

a(n) = 3^(n+1)-2^(n+1)+17*a(n-1)-70*a(n-2). - Vincenzo Librandi, May 08 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-7*x)*(1-10*x)), {x, 0, 20}], x] (* Harvey P. Dale, Sep 06 2021 *)
(* Alternative: *)
LinearRecurrence[{22, -161, 452, -420}, {1, 22, 323, 4016}, 20] (* Harvey P. Dale, Sep 06 2021 *)
(* Alternative: *)
a[0]=1; a[1]=22; a[n_]:=a[n]=3^(n+1)-2^(n+1)+17*a[n-1]-70*a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, May 08 2026 *)

Prog

(Magma) I:=[1, 22]; [n le 2 select I[n] else 3^n-2^n+17*Self(n-1)-70*Self(n-2): n in [1..23]]; // Vincenzo Librandi, May 08 2026

Crossrefs

Sequence in context: A025948 A021904 A022343 * A288576 A020571 A021874

Adjacent sequences: A025942 A025943 A025944 * A025946 A025947 A025948

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 08 2026

Status

approved