OFFSET
0,3
COMMENTS
U_20(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.
FORMULA
E.g.f.: g(x)^2 where g(x) is the e.g.f. of A070190. - Andrew Howroyd, Nov 01 2018
a(n) ~ 2^(2*n) * 5^(n+3) / (Pi^4 * n^4). - Vaclav Kotesovec, Apr 30 2024
PROG
(PARI) seq(n)={Vec(serlaplace(sum(k=0, n, if(k, 2, 1)*(x^k*besseli(k, 2*x + O(x^(n-k+1)))/k!)^5)^2))} \\ Andrew Howroyd, Nov 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Simon Plouffe, Oct 30 2011
STATUS
approved