A025940 Expansion of 1/((1-2x)(1-3x)(1-6x)(1-10x)).

1, 21, 295, 3525, 38911, 411741, 4255255, 43385925, 438878671, 4418961261, 44370835015, 444796211925, 4454490876031, 44584086067581, 446075938835575, 4462169900295525, 44630162203602991, 446352401627074701

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21, -146, 396, -360).

Formula

a(n) = -9*6^n/2 +3^(n+2)/7 -2^(n-2) +125*10^n/28. - R. J. Mathar, Jun 04 2013

a(n) = 21*a(n-1)-146*a(n-2)+ 396*a(n-3)- 360*a(n-4), with a(0)=1, a(1)=21, a(2)=295, a(3)=3525. - Harvey P. Dale, Jul 26 2014

Maple

seq(-9*6^n/2 +3^(n+2)/7 -2^(n-2) +125*10^n/28, n=0..100); # Robert Israel, Jul 27 2014

Mathematica

CoefficientList[Series[1/((1-2x)(1-3x)(1-6x)(1-10x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{21, -146, 396, -360}, {1, 21, 295, 3525}, 30] (* Harvey P. Dale, Jul 26 2014 *)

Prog

(Magma) [-9*6^n/2 +3^(n+2)/7 -2^(n-2) +125*10^n/28: n in [0..20]]; // Vincenzo Librandi, Jul 27 2014

Crossrefs

Sequence in context: A027474 A021864 A020570 * A041844 A295779 A021829

Adjacent sequences: A025937 A025938 A025939 * A025941 A025942 A025943

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved