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A243280 Expansion of log'(1/2-sqrt((5*x+2*sqrt(1-4*x)-2)/x)/2). 0
1, 3, 13, 63, 325, 1748, 9685, 54841, 315605, 1838610, 10811788, 64041706, 381525253, 2283436938, 13718099275, 82672421423, 499546587317, 3025336228390, 18357852413062, 111587292429820, 679306584310220 (list; graph; refs; listen; history; text; internal format)
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: A026715 A001850 A130525 * A000259 A007855 A193112

Adjacent sequences:  A243277 A243278 A243279 * A243281 A243282 A243283

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Jun 02 2014

STATUS

approved

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)