OFFSET
1,2
COMMENTS
a(n) is the number of birooted graphs on n labeled nodes. - Andrew Howroyd, Nov 23 2020
Old (incorrect) name was: "Number of perfect matchings of an n X (n+1) Aztec rectangle with the third vertex in the topmost row removed". See Mathematics Stack Exchange for the discussion. - Andrey Zabolotskiy, Jun 05 2022
LINKS
M. Ciucu, Enumeration of perfect matchings in graphs with reflective symmetry, J. Combin. Theory Ser. A 77 (1997), no. 1, 67-97, doi:10.1006/jcta.1996.2725.
N. Elkies, G. Kuperberg, M. Larsen and J. Propp, Alternating sign matrices and domino tilings, Journal of Algebraic Combinatorics 1 (1992), 111-132 (Part I), 219-234 (Part II); arXiv:math/9201305 [math.CO], 1992.
H. Helfgott and I. M. Gessel, Enumeration of tilings of diamonds and hexagons with defects, arXiv:math/9810143 [math.CO], 1998.
C. Krattenthaler, Schur function identities and the number of perfect matchings of Aztec holey rectangles, arXiv:math/9712204 [math.CO], 1997.
Mathematics Stack Exchange, Mistake in OEIS A103904?, 2021.
FORMULA
a(n) = 2*A095351(n). - Andrew Howroyd, Nov 23 2020
a(n) = A036289(n*(n-1)/2). - Michael Somos, Feb 28 2021
PROG
(PARI) a(n)={binomial(n, 2)*2^binomial(n, 2)} \\ Andrew Howroyd, Nov 23 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Feb 21 2005
EXTENSIONS
Name replaced by a formula, a(1) changed from 1 to 0, and entry edited by Andrey Zabolotskiy, Jun 05 2022
STATUS
approved