A025962 Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-10*x)).

1, 21, 293, 3465, 37821, 396081, 4058293, 41102985, 413760941, 4151788641, 41590878693, 416282134905, 4164721639261, 41656852053201, 416617235689493, 4166418080133225, 41665418007392781, 416660400463837761

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..950

Index entries for linear recurrences with constant coefficients, signature (21,-148,420,-400).

Formula

a(n) = -2^n/6+16*4^n/3-25*5^n/3+25*10^n/6. - R. J. Mathar, Jun 20 2013

a(n) = (4^(n+1)-2^(n+1))/2+15*a(n-1)-50*a(n-2). - Vincenzo Librandi, Jun 03 2026

E.g.f.: exp(2*x)*(25*exp(8*x) - 50*exp(3*x) + 32*exp(2*x) - 1)/6. - Stefano Spezia, Jun 10 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-4*x)*(1-5*x)*(1-10*x)), {x, 0, 20}], x] (* Harvey P. Dale, Mar 28 2024 *)
(* Alternative: *)
LinearRecurrence[{21, -148, 420, -400}, {1, 21, 293, 3465}, 20] (* Harvey P. Dale, Mar 28 2024 *)
(* Alternative: *)
a[0]=1; a[1]=21; Do[a[n]=(4^(n+1)-2^(n+1))/2+15*a[n-1]-50*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, Jun 03 2026 *)

Prog

(Magma) I:=[1, 21]; [n le 2 select I[n] else (4^n-2^n)/2+15*Self(n-1)-50*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 03 2026

Crossrefs

Sequence in context: A275359 A022291 A025944 * A181381 A081137 A027474

Adjacent sequences: A025959 A025960 A025961 * A025963 A025964 A025965

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved