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URL: https://oeis.org/A341275

⇱ A341275 - OEIS

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A341275
a(n) = 2^(n*(n-1)/2)*Product_{j=0..n-1} (4*j+2)!/(n+2*j+1)!.
1
1, 4, 60, 3328, 678912, 508035072, 1392439459840, 13965623033856000, 512247880383410995200, 68683284942451522425323520, 33654191472236763924706696888320, 60248257274480672292932706180054122496, 393994689318303735728047162574735199856230400
OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..60
Seok Hyun Byun and Mihai Ciucu, A short combinatorial proof of Di Francesco's conjecture on Aztec triangles, arXiv:2508.04545 [math.CO], 2025.
Philippe Di Francesco, Twenty Vertex model and domino tilings of the Aztec triangle, arXiv:2102.02920 [math.CO], 2021.
Frederick Huang, The 20 Vertex Model and Related Domino Tilings, Ph. D. Dissertation, UC Berkeley, 2023. See p. 1.
FORMULA
a(n) ~ exp(1/48) * Pi^(1/4) * 2^(9*n^2/2 + n/2 + 1/3) / (sqrt(Gamma(1/4)) * A^(1/4) * n^(7/48) * 3^(9*n^2/4 + 3*n/4 - 1/24)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 08 2021
MATHEMATICA
Table[2^(n*(n-1)/2) * Product[(4*j + 2)!/(n + 2*j + 1)!, {j, 0, n-1}], {n, 1, 15}] (* Vaclav Kotesovec, Feb 08 2021 *)
PROG
(PARI) a(n) = 2^(n*(n-1)/2)*prod(j=0, n-1, (4*j+2)!/(n+2*j+1)!);
CROSSREFS
Sequence in context: A012567 A132627 A229771 * A338550 A340937 A136385
KEYWORD
nonn
AUTHOR
Michel Marcus, Feb 08 2021
STATUS
approved