OFFSET
0,2
COMMENTS
Extended to a(0)-a(2) using the sum/recurrence. - Eric W. Weisstein, Oct 03 2017
LINKS
Andrew Howroyd and Vaclav Kotesovec, Table of n, a(n) for n = 0..780 (terms 3..50 from Andrew Howroyd; terms a(0..2) corrected by Georg Fischer, Jan 20 2019)
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Sun Graph
FORMULA
a(n) = A000085(n) + 2*(Sum_{ k=1..n } n * binomial(2*n-k-1, k-1) * A000085(n-k) / k). - Andrew Howroyd, Feb 28 2016, corrected by Vaclav Kotesovec, Mar 06 2016
Recurrence (for n>=7): (n-3)*a(n) = 3*(n-3)*a(n-1) + (n^2 - 4*n + 5)*a(n-2) - 3*(n-1)*a(n-3) + (n-1)*a(n-4). - Vaclav Kotesovec, Mar 06 2016
a(n) ~ exp(3*sqrt(n) - n/2 - 13/4) * n^(n/2) / sqrt(2) * (1 + 39/(8*sqrt(n))). - Vaclav Kotesovec, Mar 06 2016
MATHEMATICA
Table[Sum[(2 j - 1)!! Binomial[n, 2 j], {j, 0, n/2}] + 2 Sum[n Binomial[2 n - k - 1, k - 1] Sum[(2 j - 1)!! Binomial[n - k, 2 j], {j, 0, (n - k)/2}]/k, {k, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 06 2016 *)
Join[{1}, RecurrenceTable[{(n - 3) a[n] == 3 (n - 3) a[n - 1] + (n^2 - 4 n
+ 5) a[n - 2] - 3 (n - 1) a[n - 3] + (n - 1) a[n - 4], a[1]==3, a[2]==8, a[3]==27, a[4] == 100}, a, {n, 1, 20}]] (* Eric W. Weisstein, Oct 03 2017, amended by Georg Fischer, Dec 05 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 11 2011
EXTENSIONS
a(7)-a(20) from Andrew Howroyd, Feb 28 2016
a(0)-a(2) from Eric W. Weisstein, Oct 03 2017
STATUS
approved