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A243204 Expansion of 2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x))) * sqrt(1-4*x)). 1
1, 2, 8, 35, 160, 752, 3605, 17544, 86400, 429605, 2153008, 10860720, 55086421, 280692440, 1435868960, 7369703660, 37934443008, 195748568256, 1012292239955, 5244933087000, 27220980100160, 141486701601630 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..n} binomial(2*k-1,k)*binomial(2*n-k-1,n-k)).

G.f.: A(x) = x*F'(x)/F(x), where F(x)=x*C(x)*C(x*C(x)), C(x) is g.f. of A000108.

a(n) ~ 2^(4*n-3/2) / (sqrt(Pi*n) * 3^(n-1/2)). - Vaclav Kotesovec, Jun 02 2014

MATHEMATICA

CoefficientList[Series[2*x / (Sqrt[1-4*x] + Sqrt[-1+2*Sqrt[1-4*x]] *Sqrt[1-4*x] + 8*x-2), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 02 2014 *)

PROG

(Maxima)

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

(PARI) x='x+O('x^50); Vec(2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x)))*sqrt(1-4*x))) \\ G. C. Greubel, Jun 01 2017

CROSSREFS

Cf. A000108, A121988.

Sequence in context: A037618 A184786 A082759 * A279013 A137265 A303070

Adjacent sequences:  A243201 A243202 A243203 * A243205 A243206 A243207

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Jun 01 2014

STATUS

approved

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Last modified January 21 19:47 EST 2019. Contains 319350 sequences. (Running on oeis4.)