A025933 Expansion of 1/((1-2*x)*(1-3*x)*(1-5*x)*(1-9*x)).

1, 19, 240, 2570, 25391, 240489, 2226310, 20352640, 184772181, 1670999759, 15079423580, 135917468310, 1224272081371, 11023527831829, 99237160300050, 893261534749580, 8039989402000961, 72363082951440699, 651283639391863720, 5861632222156996450, 52755087348022338951, 474797772906624770369

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-121,309,-270).

Formula

a(n) = (9^(n+3)-7*5^(n+3)+14*3^(n+3)-8*2^(n+3))/168. - Yahia Kahloune, May 08 2013

a(n) = 3^(n+1)-2^(n+1)+14*a(n-1)-45*a(n-2). - Vincenzo Librandi, Apr 20 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-5x)(1-9x)), {x, 0, 25}], x] (* or *) LinearRecurrence[{19, -121, 309, -270}, {1, 19, 240, 2570}, 25] (* Harvey P. Dale, Dec 26 2021 *)
a[0]=1; a[1]=19; a[n_]:=a[n]=3^(n+1)-2^(n+1)+14*a[n-1]-45*a[n-2]; Table[a[n], {n, 0, 25}] (* Vincenzo Librandi, Apr 20 2026 *)

Prog

(PARI) my(x='x+O('x^25)); Vec(1/((1-2*x)*(1-3*x)*(1-5*x)*(1-9*x))) \\ Joerg Arndt, May 08 2013
(Magma) I:=[1, 19]; [n le 2 select I[n] else 3^n-2^n+14*Self(n-1)-45*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 20 2026

Crossrefs

Sequence in context: A142615 A021814 A299864 * A107203 A021544 A021772

Adjacent sequences: A025930 A025931 A025932 * A025934 A025935 A025936

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 20 2026

Status

approved