A186812 Expansion of 1/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-x).

1, 1, 3, 8, 21, 53, 135, 346, 886, 2266, 5796, 14828, 37935, 97047, 248269, 635134, 1624833, 4156729, 10633949, 27204296, 69595384, 178042372, 455476844, 1165223500, 2980932677, 7625970145, 19509135875, 49909241100, 127680301337, 326638093273, 835621805859

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

Index entries for linear recurrences with constant coefficients, signature (1,2,3,4,3,1)

Formula

a(n+1) = sum(m=1..n, sum(k=m..n, binomial(k,n-k) *sum(j=0..m, binomial(m,j) *binomial(j,k-3*m+2*j)))).

Mathematica

CoefficientList[Series[1/(1-x^6-3x^5-4x^4-3x^3-2x^2-x), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 2, 3, 4, 3, 1}, {1, 1, 3, 8, 21, 53}, 30] (* Harvey P. Dale, Aug 30 2014 *)

Crossrefs

Sequence in context: A039671 A267946 A166287 * A027930 A038200 A291039

Adjacent sequences: A186809 A186810 A186811 * A186813 A186814 A186815

Keyword

nonn,easy

Author

Vladimir Kruchinin, Feb 28 2011

Extensions

More terms from Harvey P. Dale, Aug 30 2014

Status

approved