A025445 Expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)*(1-7*x)).

1, 16, 167, 1454, 11529, 86772, 633739, 4547818, 32300477, 228024368, 1604029791, 11260172742, 78950652145, 553177103404, 3874344193523, 27128870214626, 189936063951333, 1329688724613480, 9308367341848135, 65160759956887870, 456134084412274841

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (16,-89,206,-168).

Formula

a(n) = (2*7^(n+3) - 5*4^(n+4) + 10*3^(n+4) - 3*2^(n+5))/120. - Yahia Kahloune, May 30 2013

a(0) = 1, a(1) = 16, a(2) = 167, a(3) = 1454, a(n) = 16*a(n-1) - 89*a(n-2) + 206*a(n-3) - 168*a(n-4). - Harvey P. Dale, Dec 07 2015

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-4x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{16, -89, 206, -168}, {1, 16, 167, 1454}, 30] (* Harvey P. Dale, Dec 07 2015 *)
a[1]=1; a[2]=16; a[n_]:=a[n]=3^n-2^n+11 a[n-1]-28 a[n-2]; Table[a[n], {n, 1, 25}] (* Vincenzo Librandi, Apr 14 2026 *)

Prog

(Magma) I:=[1, 16]; [n le 2 select I[n] else 3^n - 2^n + 11*Self(n-1)-28*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 14 2026

Crossrefs

Sequence in context: A246057 A265598 A021744 * A022740 A394274 A205247

Adjacent sequences: A025442 A025443 A025444 * A025446 A025447 A025448

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 14 2026

Status

approved