A093526 - OEIS

A093526

Numerators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.

1, 1, 5, 7, 42, 22, 429, 715, 4862, 8398, 58786, 52003, 742900, 1337220, 646323, 17678835, 129644790, 79606450, 1767263190, 328206021, 8155422340, 45741281820, 343059613650, 107492012277, 4861946401452, 9183676536076

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Disk Line Picking

FORMULA

a(k) = Numerator[(2*Gamma[3 + n])/((2 + n)*Gamma[2 + n/2]*Gamma[3 + n/2])] for n = 2k.

a(n) = denominator((n+1)/C(n+1)). - Paul Barry, Nov 17 2004

a(n) = A195686(n+1) / (n+2). - Peter Luschny, Oct 06 2011

EXAMPLE

1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...

MAPLE

A195686 := n -> binomial(2*n, n) / igcd(n, binomial(2*n, n));

A093526 := n -> A195686(n+1)/(n+2); # Peter Luschny, Oct 06 2011

MATHEMATICA

a[n_] := Binomial[2(n+1), n+1]/((n+2) GCD[n+1, Binomial[2(n+1), n+1]]);

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jul 30 2018, after Peter Luschny *)

PROG

(PARI) a(n) = denominator((n+1)*(n+2)/binomial(2*n+2, n+1)); \\ Michel Marcus, Jul 30 2018

CROSSREFS

Cf. A093070, A093527, A093528, A093529.

Cf. A098512, A000108.

Sequence in context: A120298 A178342 A117751 * A098512 A234040 A292010

Adjacent sequences: A093523 A093524 A093525 * A093527 A093528 A093529

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Mar 30 2004

STATUS

approved