A239305 Expansion of (4*x^4-5*x^3-x^2+3*x-1) / (2*x^5+3*x^4-4*x^3-3*x^2+4*x-1).

1, 1, 2, 6, 13, 31, 69, 153, 332, 712, 1509, 3169, 6603, 13669, 28142, 57674, 117741, 239587, 486193, 984353, 1989056, 4012636, 8083717, 16266181, 32698903, 65678221, 131827874, 264447198, 530221357, 1062664807, 2129046429

Offset

0,3

Links

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

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

Formula

a(n) = sum(k=0..n, ((k*n-1)*sum(i=0..n-k, 2^i*binomial(k+1,n-k-i)*binomial(k+i,k)*(-1)^(n-i+1)))/(k+1)).

G.f.: x*(x-1)*(4*x^3-x^2-2*x+1) / ( (-1+2*x)*(x^2+x-1)^2 ).

Mathematica

CoefficientList[Series[(4*x^4-5*x^3-x^2+3*x-1) / (2*x^5+3*x^4-4*x^3-3*x^2+4*x-1), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 15 2014 *)

Prog

(Maxima)
a(n):=sum(((k*n-1)*sum(2^i*binomial(k+1, n-k-i)*binomial(k+i, k)*(-1)^(n-i+1), i, 0, n-k))/(k+1), k, 0, n);

Crossrefs

Sequence in context: A369584 A336875 A219753 * A018013 A263899 A062424

Adjacent sequences: A239302 A239303 A239304 * A239306 A239307 A239308

Keyword

nonn,easy

Author

Vladimir Kruchinin, Mar 14 2014

Status

approved