A103904 a(n) = n*(n-1)/2 * 2^(n*(n-1)/2).

0, 2, 24, 384, 10240, 491520, 44040192, 7516192768, 2473901162496, 1583296743997440, 1981583836043018240, 4869940435459321626624, 23574053482485268906770432, 225305087149939210031640608768

Offset: 1

Author

Ralf Stephan, Feb 21 2005

Keywords

• nonn

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.

Crossrefs

Cf. A000217, A006125, A038094, A095340, A095351, A134401, A036289, A303831.

Programs

PARI

a(n)={binomial(n,2)*2^binomial(n,2)} \\ Andrew Howroyd, Nov 23 2020

Formula

a(n) = A000217(n-1) * A006125(n).

a(n) = 2*A095351(n). - Andrew Howroyd, Nov 23 2020

a(n) = A036289(n*(n-1)/2). - Michael Somos, Feb 28 2021

Extensions

Name replaced by a formula, a(1) changed from 1 to 0, and entry edited by Andrey Zabolotskiy, Jun 05 2022