cp's OEIS Frontend

A198804 Number of closed paths of length n whose steps are 16th roots of unity, U_16(n).

%I A198804 #19 Feb 06 2024 08:10:35
%S A198804 1,0,16,0,720,0,50560,0,4649680,0,514031616,0,64941883776,0,
%T A198804 9071319628800,0,1369263687414480,0,219705672931613440,0,
%U A198804 37024402443528248320,0,6493814173413849784320,0,1177304833671218302960000,0,219456611569479963675136000,0
%N A198804 Number of closed paths of length n whose steps are 16th roots of unity, U_16(n).
%C A198804 U_16(n), (comment in article) : For each m >= 1, the sequence (U_m(N)), N >= 0 is P-recursive but is not algebraic when m > 2.
%H A198804 Andrew Howroyd, <a href="/A198804/b198804.txt">Table of n, a(n) for n = 0..200</a>
%H A198804 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 A198804 E.g.f.: ( Sum_{n>=0} x^(2*n)/n!^2 )^8. - _Paul D. Hanna_, Oct 30 2011
%F A198804 E.g.f.: g(x)^8 where g(x) is the e.g.f. of A126869. - _Andrew Howroyd_, Nov 01 2018
%o A198804 (PARI) {a(n)=n!*polcoeff(sum(m=0,n,x^(2*m)/m!^2+x*O(x^n))^8,n)}
%Y A198804 Cf. A000984, A002894, A039699, A126869.
%K A198804 nonn
%O A198804 0,3
%A A198804 _Simon Plouffe_, Oct 30 2011