A101497 Expansion of (1-x^2)/(1-2x+2x^3+x^4).

1, 2, 3, 4, 3, -2, -15, -40, -79, -126, -157, -116, 99, 638, 1665, 3248, 5121, 6274, 4387, -4716, -27101, -69250, -133455, -207992, -250383, -164606, 220227, 1149212, 2878019, 5480190, 8441729, 9978208, 6118017, -10127614, -48653373, -119520988, -224904765, -342375170

Offset

0,2

Comments

Results from applying a Chebyshev transform after an inverse Catalan transform to 1/(1-2x). The inverse Catalan transform maps g(x)->g(x(1-x)) while the Chebyshev transform maps h(x)->(1/(1+x^2))h(x/(1+x^2)).

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,-1)

Formula

a(n)=2a(n-1)-2a(n-3)-a(n-4); a(n)=sum{k=0..floor(n/2), sum{j=0..floor((n-2k)/2), C(n-k, k)C(n-2k-j, j)2^(n-2k-j)}}.

Mathematica

CoefficientList[Series[(1-x^2)/(1-2x+2x^3+x^4), {x, 0, 80}], x]  (* Harvey P. Dale, Mar 14 2011 *)

Crossrefs

Sequence in context: A111880 A348599 A306461 * A274007 A065870 A123699

Adjacent sequences: A101494 A101495 A101496 * A101498 A101499 A101500

Keyword

easy,sign

Author

Paul Barry, Dec 04 2004

Status

approved