A091903 Expansion of x/((1+5*x)*(1-10*x)).

0, 1, 5, 75, 625, 6875, 65625, 671875, 6640625, 66796875, 666015625, 6669921875, 66650390625, 666748046875, 6666259765625, 66668701171875, 666656494140625, 6666717529296875, 66666412353515625, 666667938232421875, 6666660308837890625, 66666698455810546875, 666666507720947265625

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,50).

Formula

a(n) = A091883(n+1)/50.

Limit_{n->oo} a(n)/a(n+1) = 1/10.

a(n) = 10^n/15 - (-5)^n/15.

a(0) = 0, a(1) = 1, a(n) = 5*a(n-1) + 50*a(n-2). - Harvey P. Dale, Mar 13 2013

a(n) = 5^(n-1)*A001045(n). - R. J. Mathar, Mar 08 2021

E.g.f.: (exp(10*x) - exp(-5*x))/15. - Amiram Eldar, Feb 20 2026

Mathematica

CoefficientList[Series[x/((1+5x)(1-10x)), {x, 0, 30}], x] (* Harvey P. Dale, Mar 13 2013 *)
(* Alternative: *)
LinearRecurrence[ {5, 50}, {0, 1}, 30] (* Harvey P. Dale, Mar 13 2013 *)

Crossrefs

Cf. A001045, A091883.

Sequence in context: A216093 A151752 A127212 * A105490 A307823 A105494

Adjacent sequences: A091900 A091901 A091902 * A091904 A091905 A091906

Keyword

easy,nonn,changed

Author

Paul Barry, Feb 10 2004

Status

approved