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A255688 G.f.: (2*x+1)/(2*sqrt(4*x^2-8*x+1)) + 1/2. 1
1, 3, 15, 90, 579, 3858, 26262, 181380, 1265955, 8906706, 63058530, 448716876, 3206387790, 22992276180, 165364807308, 1192393813320, 8617219956003, 62397513984210, 452607991376490, 3288138397237884, 23921128800374874 (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_{i=0..n} 2^(n-i)*binomial(n,i)*binomial(n+i-1,i)).

a(n) ~ 3^(1/4) * 2^(n-1) * (2+sqrt(3))^n / sqrt(Pi*n). - Vaclav Kotesovec, Mar 15 2015

a(n) = 2^n*hypergeom([-n, n], [1], -1/2). - Peter Luschny, Mar 15 2015

D-finite with recurrence: n*a(n) -6*n*a(n-1) +12*(-n+3)*a(n-2) +8*(n-3)*a(n-3)=0. - R. J. Mathar, Jan 25 2020

MATHEMATICA

CoefficientList[Series[(2*x+1)/(2*Sqrt[4*x^2-8*x+1])+1/2, {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 15 2015 *)

PROG

(Maxima)

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

(Sage)

a = lambda n: 2^n*hypergeometric([-n, n], [1], -1/2).simplify()

[a(n) for n in range(21)] # Peter Luschny, Mar 15 2015

(PARI) x='x+O('x^50); Vec((2*x+1)/(2*sqrt(4*x^2-8*x+1)) + 1/2) \\ G. C. Greubel, Jun 03 2017

CROSSREFS

Sequence in context: A074550 A205576 A173695 * A025748 A097188 A271930

Adjacent sequences:  A255685 A255686 A255687 * A255689 A255690 A255691

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Mar 15 2015

STATUS

approved

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Last modified July 8 03:25 EDT 2020. Contains 335503 sequences. (Running on oeis4.)