OFFSET
0,2
COMMENTS
For positive n, a(n) equals the permanent of the n X n matrix with 2's along the main diagonal and the upper diagonal, and 1's everywhere else. - John M. Campbell, Jul 09 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Veronica Bitonti, Bishal Deb, and Alan D. Sokal, Thron-type continued fractions (T-fractions) for some classes of increasing trees, arXiv:2412.10214 [math.CO], 2024. See p. 58.
FORMULA
G.f.: 1/(1 -x -x/(1 -x -x/(1 -x -2*x/(1 -x -2*x/(1 -x -3*x/(1 -x -3*x/(1 - ... (continued fraction);
a(n) = Sum_{k=0..n} binomial(2*n-k, k)*(n-k)!.
a(n) = Sum_{k=0..n} binomial(n+k, 2*k)*k!. - Paul Barry, May 28 2009
a(n) = (n+1)*a(n-1) -(n-3)*a(n-2) -a(n-3). - R. J. Mathar, Nov 15 2012
a(n) ~ exp(2) * n!. - Vaclav Kotesovec, Feb 08 2014
MATHEMATICA
Table[Sum[Binomial[2*n-k, k]*(n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)
PROG
(Sage) [sum(binomial(2*n-k, k)*factorial(n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 05 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jan 29 2009
STATUS
approved