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A101004 See formula line. 1

%I

%S 1,13,263,7518,280074,12895572,707902740,45152821872,3282497058384,

%T 267944580145440,24268165166553120,2415271958048304000,

%U 262018936450492859520,30774091302535254992640,3890462788950375951532800,526745212429645673433446400,76046696235437224473872640000

%N See formula line.

%H Vaclav Kotesovec, <a href="/A101004/b101004.txt">Table of n, a(n) for n = 1..328</a>

%H David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, <a href="http://arxiv.org/abs/0801.0891">Elliptic integral evaluations of Bessel moments</a>, arXiv:0801.0891

%F Let h_n = Sum_{ j=1..n } binomial(n,j)^2*binomial(2*j,j)*Sum_{ i=0..j-1 } 2/(n-i). Then a(n) = n!*h_n/4.

%F a(n) ~ n! * log(3) * 3^(2*n + 3/2) / (8*Pi*n). - _Vaclav Kotesovec_, Oct 06 2019

%p h := n-> add(binomial(n,j)^2*binomial(2*j,j)*add( 2/(n-i), i=0..j-1), j=1..n); [seq(n!*h(n)/4, n=1..30)];

%t h[n_] := Sum[Binomial[n, j]^2*Binomial[2*j, j]*Sum[2/(n-i), {i, 0, j-1}], {j, 1, n}]; a[n_] := n!*h[n]/4; (* _Jean-Fran├žois Alcover_, May 31 2016 *)

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Jan 20 2008, Jan 25 2008

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Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)