A025986 Expansion of 1/((1-2*x)*(1-5*x)*(1-6*x)*(1-7*x)).

1, 20, 257, 2704, 25389, 221676, 1841449, 14758568, 115171397, 880623172, 6627177921, 49248518592, 362296167325, 2643446894108, 19158543110873, 138087153497176, 990728497913973, 7081081591668084, 50449821607899505, 358474043196164720, 2541428999737064141

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-143,424,-420).

Formula

a(n) = -2*2^n/15+125*5^n/6-54*6^n/1+343*7^n/10. - R. J. Mathar, Jun 20 2013

a(n) = (5^(n+1)-2^(n+1))/3+13*a(n-1)-42*a(n-2). - Vincenzo Librandi, Jul 05 2026

E.g.f.: exp(2*x)*(1029*exp(5*x)-1620*exp(4*x)+625*exp(3*x)-4)/30. - Stefano Spezia, Sep 29 2022

Mathematica

CoefficientList[Series[1/((1-2x)(1-5x)(1-6x)(1-7x)), {x, 0, 20}], x] (* Harvey P. Dale, Oct 10 2017 *)
(* Alternative: *)
LinearRecurrence[{20, -143, 424, -420}, {1, 20, 257, 2704}, 20] (* Harvey P. Dale, Oct 10 2017 *)

Prog

(Magma) I:=[1, 20]; [n le 2 select I[n] else (5^n-2^n)/3+13*Self(n-1)-42*Self(n-2): n in [1..21]]; // Vincenzo Librandi, Jul 05 2026

Crossrefs

Cf. A028027, A028032.

Sequence in context: A387276 A028032 A348055 * A028027 A268764 A081244

Adjacent sequences: A025983 A025984 A025985 * A025987 A025988 A025989

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jul 05 2026

Status

approved