A198800 Number of closed paths of length n whose steps are 20th roots of unity, U_20(n).

1, 0, 20, 0, 1140, 480, 102800, 151200, 12310900, 38707200, 1812247920, 9574488000, 313983978000, 2391608419200, 62051403928800, 611744666332800, 13627749414064500, 160896284989440000, 3253345101771050000, 43527416858084016000, 829176006298475046640

Offset: 0

Author

Simon Plouffe, Oct 30 2011

Keywords

• nonn

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.

Crossrefs

Cf. A070190, A198808.

Programs

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

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