OFFSET
0,3
COMMENTS
A modification of e.g.f. of A002898, where the exponent of I, which is 3, is here replaced by 5.
U_10(n), in Labelle-Lacasse paper, number of closed paths of length n whose steps are 10th roots of unity.
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
a(n) ~ 5^(3/2) * 10^n / (4*Pi^2*n^2). - Vaclav Kotesovec, Jun 08 2021
MATHEMATICA
With[{nmax = 25}, CoefficientList[Series[BesselI[0, 2*x]^5 + 2*Sum[BesselI[k, 2*x]^5, {k, 1, 2*nmax}], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 05 2018 *)
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)))} \\ Andrew Howroyd, Nov 01 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Apr 26 2002
STATUS
approved