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Number of closed paths of length 19n whose steps are 19th roots of unity.
1

%I #19 Feb 06 2024 08:12:50

%S 1,121645100408832000,997586474354936812896742294502400000000,

%T 66507379539349211518364492838558005847493108039680000000000000,

%U 11256716378122801825351385824819232115042452248916289339300576523719750000000000000000

%N Number of closed paths of length 19n whose steps are 19th roots of unity.

%C Equivalently, the number of paths of length 19n in Z^19 from {0}^19 to {n}^19. - _Andrew Howroyd_, Nov 01 2018

%H Andrew Howroyd, <a href="/A198801/b198801.txt">Table of n, a(n) for n = 0..40</a>

%H Gilbert Labelle and Annie Lacasse, <a href="https://doi.org/10.46298/dmtcs.2937">Closed paths whose steps are roots of unity</a>, in FPSAC 2011, Reykjavik, Iceland DMTCS proc. AO, 2011, 599-610.

%F a(n) = (19*n)!/(n!)^19. - _Andrew Howroyd_, Nov 01 2018

%o (PARI) a(n) = (19*n)!/(n!)^19; \\ _Andrew Howroyd_, Nov 01 2018

%Y Row n=19 of A187783, column k=19 of A089759.

%K nonn

%O 0,2

%A _Simon Plouffe_, Oct 30 2011

%E Sequence redefined and a(2)-a(4) from _Andrew Howroyd_, Nov 01 2018