A108476 Expansion of (1-4x)/(1-6x-12x^2+8x^3).

1, 2, 24, 160, 1232, 9120, 68224, 508928, 3799296, 28357120, 211662848, 1579868160, 11792306176, 88018952192, 656982441984, 4903783628800, 36602339459072, 273203580764160, 2039219289063424, 15220939987877888

Offset

0,2

Comments

In general, sum{k=0..n, sum{j=0..n, C(2(n-k),j)C(2k,j)r^j}} has expansion (1-(r+1)x)/((1+(r+3)x+(r-1)(r+3)x^2+(r-1)^3*x^3).

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (6,12,-8).

Formula

G.f.: (1-4x)/((1+2x)(1-8x+4x^2)); a(n)=6a(n-1)+12a(n-2)-8a(n-3); a(n)=sum{k=0..n, sum{j=0..n, C(2(n-k), j)C(2k, j)3^j}}.

Conjecture: a(n)=A002605(n+1)*A026150(n). [From R. J. Mathar, Jul 08 2009]

a(0)=1, a(1)=2, a(2)=24, a(n)=6*a(n-1)+12*a(n-2)-8*a(n-3) [From Harvey P. Dale, Feb 21 2012]

a(n) = (-2)^n/2 +A102591(n)/2. - R. J. Mathar, Sep 20 2012

Mathematica

CoefficientList[Series[(1-4x)/(1-6x-12x^2+8x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{6, 12, -8}, {1, 2, 24}, 30] (* Harvey P. Dale, Feb 21 2012 *)

Crossrefs

Sequence in context: A234352 A241623 A288443 * A157053 A279853 A052411

Adjacent sequences: A108473 A108474 A108475 * A108477 A108478 A108479

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved