A198806 Number of closed paths of length n whose steps are 14th roots of unity, U_14(n).

1, 0, 14, 0, 546, 0, 32900, 10080, 2570050, 2540160, 238935564, 465696000, 25142196156, 76886409600, 2900343069624, 12211317518400, 359067702643650, 1915829643087360, 47006105030584700, 300455419743198720, 6437718469449262996

Offset: 0

Author

Simon Plouffe, Oct 30 2011

Keywords

• nonn

Comments

U_14(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. A002898, A070190, A071549.

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!)^7)))} \\ Andrew Howroyd, Nov 01 2018

Formula

E.g.f.: BesselI(0,2*x)^7 + 2*Sum_{k>=1} BesselI(k,2*x)^7. - Andrew Howroyd, Nov 01 2018