login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A070190 Expansion of e.g.f. I_0(2*x)^5 + 2*Sum_{k>=1} I_k(2*x)^5, where I_n(z) are modified Bessel functions of order n. 4
1, 0, 10, 0, 270, 240, 10900, 25200, 551950, 2116800, 32458860, 169092000, 2120787900, 13427013600, 149506414200, 1075081207200, 11143223412750, 87198375264000, 865743970019500, 7171730187336000, 69416724049550020 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A002898.
Sequence in context: A089831 A221414 A326719 * A216797 A221305 A173775
KEYWORD
nonn
AUTHOR
Karol A. Penson, Apr 26 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 22 02:54 EDT 2024. Contains 371887 sequences. (Running on oeis4.)