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A102557 Denominator of the probability that 2n-dimensional Gaussian random triangle has an obtuse angle. 11
4, 32, 512, 4096, 131072, 1048576, 16777216, 134217728, 8589934592, 68719476736, 1099511627776, 8796093022208, 281474976710656, 2251799813685248, 36028797018963968, 288230376151711744, 36893488147419103232, 295147905179352825856, 4722366482869645213696, 37778931862957161709568 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Presumably this is the same as A093581? - Andrew S. Plewe, Apr 18 2007

LINKS

Robert Israel, Table of n, a(n) for n = 1..830

Eric Weisstein's World of Mathematics, Gaussian Triangle Picking

FORMULA

From Robert Israel, Sep 29 2016: (Start)

a(n) is the denominator 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(denom(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] // Denominator; Array[a, 20] (* Jean-Fran├žois Alcover, Mar 22 2019 *)

PROG

(PARI) a(n) = denominator(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. A093581, A102556, A102558, A102559.

Sequence in context: A192501 A192487 A093581 * A144935 A153511 A140179

Adjacent sequences:  A102554 A102555 A102556 * A102558 A102559 A102560

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Jan 14 2005

STATUS

approved

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Last modified November 29 11:50 EST 2020. Contains 338765 sequences. (Running on oeis4.)