A021874 Expansion of 1/((1-x)(1-4x)(1-7x)(1-10x)).

1, 22, 325, 4070, 46781, 511742, 5430405, 56516790, 580744461, 5916830062, 59935396885, 604729235110, 6084941584541, 61113049957982, 612976296281765, 6142684971387030, 61517309500479021, 615806336417543502

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (22,-159,418,-280).

Formula

a(n) = (10^(n+3) - 3*7^(n+3) + 3*4^(n+3) - 1)/162. - Yahia Kahloune, Jul 05 2013

E.g.f.: exp(x)*(1000*exp(9*x) - 1029*exp(6*x) + 192*exp(3*x) - 1)/(3!*3^3). This is d^3/dx^3 exp(x)*(exp(3*x - 1))^3/(3!*3^3); see also column m=3 of A282629 divided by 3^3. The o.g.f. is given in the name. - Wolfdieter Lang, Apr 08 2017

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{22, -159, 418, -280}, {1, 22, 325, 4070}, 30] (* Harvey P. Dale, May 13 2018 *)

Crossrefs

Cf. A000012, A002450, A016223, A282629.

Sequence in context: A025945 A288576 A020571 * A025963 A020343 A025941

Adjacent sequences: A021871 A021872 A021873 * A021875 A021876 A021877

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved