A004057 Expansion of (1-x)/( (1+x)*(1-2*x)*(1-3*x)*(1-4*x)).

1, 7, 39, 191, 875, 3843, 16423, 68887, 285219, 1170059, 4768127, 19336863, 78141883, 314953555, 1266977751, 5089412519, 20422176467, 81882328731, 328110270895, 1314184126255, 5261965982571, 21063553061987

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-17,-2,24).

Crossrefs

First differences of A099110.

Programs

Magma

[(1/30)* (20*2^n - 135*3^n + 144*4^n + (-1)^n): n in [0..30]]; // Vincenzo Librandi, Oct 08 2011

Mathematica

CoefficientList[Series[(1-x)/((1+x)(1-2x)(1-3x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{8,-17,-2,24},{1,7,39,191},30] (* Harvey P. Dale, Oct 22 2019 *)

Formula

a(n) = (1/30)*(20*2^n - 135*3^n + 144*4^n + (-1)^n).