A243280 Expansion of log'(1/2-sqrt((5*x+2*sqrt(1-4*x)-2)/x)/2).

1, 3, 13, 63, 325, 1748, 9685, 54841, 315605, 1838610, 10811788, 64041706, 381525253, 2283436938, 13718099275, 82672421423, 499546587317, 3025336228390, 18357852413062, 111587292429820, 679306584310220

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = sum(k=0..n, binomial(2*k-1,k)*binomial(2*n,n-k)).

a(n) ~ 5^(2*n+1/2) / (sqrt(3*Pi*n) * 2^(2*n+1)). - Vaclav Kotesovec, Jun 06 2014

Mathematica

Table[Sum[Binomial[2 i - 1, i] Binomial[2 n, n - i], {i, 0, n}], {n,
0, 20}] (* Wesley Ivan Hurt, Jun 06 2014 *)

Prog

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

Crossrefs

Sequence in context: A130525 A362744 A350519 * A000259 A007855 A193112

Adjacent sequences: A243277 A243278 A243279 * A243281 A243282 A243283

Keyword

nonn

Author

Vladimir Kruchinin, Jun 02 2014

Status

approved