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A102556 Numerator of the probability that 2n-dimensional Gaussian random triangle has an obtuse angle. 10
3, 15, 159, 867, 19239, 107985, 1222563, 6965835, 319153335, 1835486085, 21185534577, 122622340677, 2846090375067, 16550504577861, 192854402926251, 1125503935556763, 105252693980913879, 615999836125850637, 7219077361263238917, 42347454581722163361, 994637701798929524937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..928

Eric Weisstein's World of Mathematics, Gaussian Triangle Picking

FORMULA

From Robert Israel, Sep 29 2016: (Start)

a(n) is the numerator of p(n) = Sum_{k=n..2n-1} binomial(2n-1,k) 3^(2n-k)/4^(2n-1).

-(6n+3)p(n)+(14n+11)p(n+1)-(8n+8)p(n+2)=0 for n >= 1.

G.f. of p(n):  3x(1-1/sqrt(4-3x))/(2-2x). (End)

EXAMPLE

3/4, 15/32, 159/512, 867/4096, 19239/131072, 107985/1048576, ...

MAPLE

p:= gfun:-rectoproc({(-6*n-3)*v(n)+(14*n+11)*v(n+1)+(-8*n-8)*v(n+2), v(0) = 0, v(1) = 3/4, v(2) = 15/32}, v(n), remember):

seq(numer(p(n)), n=1..50); # Robert Israel, Sep 29 2016

MATHEMATICA

a[n_] := (3^n/4^(2n-1)) Binomial[2n-1, n] Hypergeometric2F1[1, 1-n, 1+n, -1/3] // Numerator; Array[a, 20] (* Jean-François Alcover, Mar 22 2019 *)

PROG

(PARI) a(n) = numerator(sum(k=n, 2*n-1, binomial(2*n-1, k)*3^(2*n-k)/4^(2*n-1))); \\ Michel Marcus, Mar 23 2019

CROSSREFS

Cf. A102557, A102558, A102559.

Sequence in context: A195226 A264558 A136519 * A016065 A005016 A304998

Adjacent sequences:  A102553 A102554 A102555 * A102557 A102558 A102559

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Jan 14 2005

STATUS

approved

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Last modified May 15 10:34 EDT 2021. Contains 343909 sequences. (Running on oeis4.)