A025976 Expansion of 1/((1-2*x)*(1-4*x)*(1-8*x)*(1-9*x)).

1, 23, 347, 4363, 49683, 532491, 5483299, 54909371, 538792595, 5206523179, 49719923331, 470377414299, 4416615113587, 41215417310987, 382666342963043, 3537819931431547, 32590970730866259, 299323501721262315, 2741949774077780035, 25061854585146663515

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-182,568,-576).

Formula

a(n) = -2*2^n/21 + 8*4^n/5 - 64*8^n/3 + 729*9^n/35. - R. J. Mathar, Jun 20 2013

a(0)=1, a(1)=23, a(2)=347, a(3)=4363, a(n) = 23*a(n-1)-182*a(n-2)+568*a(n-3)-576*a(n-4). - Harvey P. Dale, Sep 11 2013

a(n) = (4^(n+1)-2^(n+1))/2+17*a(n-1)-72*a(n-2). - Vincenzo Librandi, Jun 29 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-8x)(1-9x)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 11 2013 *)
(* Alternative: *)
LinearRecurrence[{23, -182, 568, -576}, {1, 23, 347, 4363}, 30] (* Harvey P. Dale, Sep 11 2013 *)

Prog

(Magma) [n le 2 select I[n] else (4^n-2^n)/2+17*Self(n-1)-72*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 29 2026

Crossrefs

Sequence in context: A028035 A077309 A042016 * A025989 A125480 A023950

Adjacent sequences: A025973 A025974 A025975 * A025977 A025978 A025979

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 29 2026

Status

approved