This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A103904 #21 Jun 05 2022 08:26:02
%S A103904 0,2,24,384,10240,491520,44040192,7516192768,2473901162496,
%T A103904 1583296743997440,1981583836043018240,4869940435459321626624,
%U A103904 23574053482485268906770432,225305087149939210031640608768
%N A103904 a(n) = n*(n-1)/2 * 2^(n*(n-1)/2).
%C A103904 a(n) is the number of birooted graphs on n labeled nodes. - _Andrew Howroyd_, Nov 23 2020
%C A103904 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
%H A103904 M. Ciucu, <a href="https://mciucu.pages.iu.edu/symmgraphs.pdf">Enumeration of perfect matchings in graphs with reflective symmetry</a>, J. Combin. Theory Ser. A 77 (1997), no. 1, 67-97, doi:<a href="https://doi.org/10.1006/jcta.1996.2725">10.1006/jcta.1996.2725</a>.
%H A103904 N. Elkies, G. Kuperberg, M. Larsen and J. Propp, Alternating sign matrices and domino tilings, Journal of Algebraic Combinatorics 1 (1992), <a href="https://doi.org/10.1023/A:1022420103267">111-132 (Part I)</a>, <a href="https://doi.org/10.1023/A:1022483817303">219-234 (Part II)</a>; arXiv:<a href="https://arxiv.org/abs/math/9201305">math/9201305</a> [math.CO], 1992.
%H A103904 H. Helfgott and I. M. Gessel, <a href="https://arxiv.org/abs/math/9810143">Enumeration of tilings of diamonds and hexagons with defects</a>, arXiv:math/9810143 [math.CO], 1998.
%H A103904 C. Krattenthaler, <a href="https://arxiv.org/abs/math/9712204">Schur function identities and the number of perfect matchings of Aztec holey rectangles</a>, arXiv:math/9712204 [math.CO], 1997.
%H A103904 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/4043123/mistake-in-oeis-a103904">Mistake in OEIS A103904?</a>, 2021.
%F A103904 a(n) = A000217(n-1) * A006125(n).
%F A103904 a(n) = 2*A095351(n). - _Andrew Howroyd_, Nov 23 2020
%F A103904 a(n) = A036289(n*(n-1)/2). - _Michael Somos_, Feb 28 2021
%o A103904 (PARI) a(n)={binomial(n,2)*2^binomial(n,2)} \\ _Andrew Howroyd_, Nov 23 2020
%Y A103904 Cf. A000217, A006125, A038094, A095340, A095351, A134401, A036289, A303831.
%K A103904 nonn
%O A103904 1,2
%A A103904 _Ralf Stephan_, Feb 21 2005
%E A103904 Name replaced by a formula, a(1) changed from 1 to 0, and entry edited by _Andrey Zabolotskiy_, Jun 05 2022