A101004 See formula line.

1, 13, 263, 7518, 280074, 12895572, 707902740, 45152821872, 3282497058384, 267944580145440, 24268165166553120, 2415271958048304000, 262018936450492859520, 30774091302535254992640, 3890462788950375951532800, 526745212429645673433446400, 76046696235437224473872640000

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..328

David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891

Formula

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.

a(n) ~ n! * log(3) * 3^(2*n + 3/2) / (8*Pi*n). - Vaclav Kotesovec, Oct 06 2019

Maple

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)];

Mathematica

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-François Alcover, May 31 2016 *)

Crossrefs

Sequence in context: A034242 A142811 A034833 * A340936 A142931 A142262

Adjacent sequences: A101001 A101002 A101003 * A101005 A101006 A101007

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 20 2008, Jan 25 2008

Status

approved