A293915 Number of linear chord diagrams having n chords and minimal chord length two.

1, 4, 26, 230, 2509, 32422, 484180, 8203519, 155460169, 3257843351, 74802301553, 1867393802229, 50358879172771, 1458899632505052, 45185432509804438, 1489952528266230695, 52112346134820625126, 1926974225717684659004, 75110765705496454871866

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..404

Formula

Recurrence: (24*n^2 - 182*n + 339)*a(n) = (96*n^3 - 800*n^2 + 1894*n - 991)*a(n-1) - (96*n^4 - 824*n^3 + 1804*n^2 + 650*n - 3571)*a(n-2) + 2*(144*n^4 - 1788*n^3 + 8032*n^2 - 15489*n + 10821)*a(n-3) - 2*(144*n^4 - 2028*n^3 + 10452*n^2 - 23337*n + 18994)*a(n-4) + (96*n^4 - 1592*n^3 + 9452*n^2 - 23794*n + 21419)*a(n-5) + (96*n^3 - 1040*n^2 + 3550*n - 3841)*a(n-6) + (24*n^2 - 134*n + 181)*a(n-7). - Vaclav Kotesovec, Oct 25 2017

a(n) ~ (exp(-1) - exp(-2)) * 2^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Oct 25 2017

Crossrefs

Column k=2 of A293881.

Sequence in context: A291847 A168448 A105616 * A107879 A066224 A227917

Adjacent sequences: A293912 A293913 A293914 * A293916 A293917 A293918

Keyword

nonn

Author

Alois P. Heinz, Oct 19 2017

Status

approved