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A198804
Number of closed paths of length n whose steps are 16th roots of unity, U_16(n).
1
1, 0, 16, 0, 720, 0, 50560, 0, 4649680, 0, 514031616, 0, 64941883776, 0, 9071319628800, 0, 1369263687414480, 0, 219705672931613440, 0, 37024402443528248320, 0, 6493814173413849784320, 0, 1177304833671218302960000, 0, 219456611569479963675136000, 0
OFFSET
0,3
COMMENTS
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.
LINKS
Gilbert Labelle and Annie Lacasse, Closed paths whose steps are roots of unity, in FPSAC 2011, Reykjavik, Iceland DMTCS proc. AO, 2011, 599-610.
FORMULA
E.g.f.: ( Sum_{n>=0} x^(2*n)/n!^2 )^8. - Paul D. Hanna, Oct 30 2011
E.g.f.: g(x)^8 where g(x) is the e.g.f. of A126869. - Andrew Howroyd, Nov 01 2018
PROG
(PARI) {a(n)=n!*polcoeff(sum(m=0, n, x^(2*m)/m!^2+x*O(x^n))^8, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Plouffe, Oct 30 2011
STATUS
approved