A025959 Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-7*x)).

1, 18, 209, 1998, 17157, 137970, 1063273, 7962966, 58471853, 423482202, 3037367697, 21634921854, 153344743189, 1083048862914, 7630057197881, 53656123623462, 376830071424765, 2644030889883306, 18539455617424225, 129932936018464590, 910316484633934181, 6376153851051874578

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-115,306,-280).

Formula

a(n) = -4*2^n/15+32*4^n/3-125*5^n/6+343*7^n/30. - R. J. Mathar, Jun 20 2013

a(n) = (4^n-2^n)/2+12*a(n-1)-35*a(n-2). - Vincenzo Librandi, Jun 01 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-4*x)*(1-5*x)*(1-7*x)), {x, 0, 20}], x] (* Harvey P. Dale, Jan 11 2026 *)
(* Alternative: *)
LinearRecurrence[{18, -115, 306, -280}, {1, 18, 209, 1998}, 20] (* Harvey P. Dale, Jan 11 2026 *)
(* Alternative: *)
a[0]=1; a[1]=18; Do[a[n]=(4^(n+1)-2^(n+1))/2+12*a[n-1]-35*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, Jun 01 2026 *)

Prog

(Magma) I:=[1, 18]; [n le 2 select I[n] else (4^n-2^n)/2+12*Self(n-1)-35*Self(n-2): n in [1..22]]; // Vincenzo Librandi, Jun 01 2026

Crossrefs

Sequence in context: A055528 A304202 A298988 * A229270 A261484 A004323

Adjacent sequences: A025956 A025957 A025958 * A025960 A025961 A025962

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 01 2026

Status

approved