A190788 Expansion of ((x-1)*sqrt(1-4*x^2))/((x-1)*sqrt(1-4*x^2)+x).

1, 1, 2, 6, 14, 38, 94, 248, 628, 1638, 4190, 10872, 27940, 72316, 186260, 481488, 1241512, 3207302, 8274646, 21369496, 55148068, 142396436, 367537484, 948920560, 2449445432, 6323741404, 16324167564, 42143003504

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

a(n)=sum(k=1..n, sum(i=0..(n-k)/2, binomial((2*i+k-2)/2,i)*4^i*binomial(n-2*i-1,k-1))), n>0, a(0)=1.

Conjecture D-finite with recurrence: (-n+1)*a(n) +(3*n-5)*a(n-1) +2*(3*n-7)*a(n-2) +4*(-6*n+19)*a(n-3) +4*(n-3)*a(n-4) +4*(11*n-53)*a(n-5) +16*(-3*n+16)*a(n-6) +16*(n-6)*a(n-7)=0. - R. J. Mathar, Nov 28 2013

Mathematica

CoefficientList[Series[((x-1)Sqrt[1-4x^2])/((x-1)Sqrt[1-4x^2]+x), {x, 0, 60}], x] (* Harvey P. Dale, May 24 2011 *)

Prog

(Maxima)
a(n):=sum(sum(binomial((2*i+k-2)/2, i)*4^i*binomial(n-2*i-1, k-1), i, 0, (n-k)/2), k, 1, n);

Crossrefs

Sequence in context: A100067 A026597 A122112 * A168259 A275208 A000634

Adjacent sequences: A190785 A190786 A190787 * A190789 A190790 A190791

Keyword

nonn

Author

Vladimir Kruchinin, May 19 2011

Status

approved