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

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

Author

Simon Plouffe, Oct 30 2011

Keywords

• nonn

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

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Gilbert Labelle and Annie Lacasse, Closed paths whose steps are roots of unity, in FPSAC 2011, Reykjavik, Iceland DMTCS proc. AO, 2011, 599-610.

Crossrefs

Cf. A000984, A002894, A039699, A126869.

Programs

PARI

{a(n)=n!*polcoeff(sum(m=0,n,x^(2*m)/m!^2+x*O(x^n))^8,n)}

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