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.

1, 0, 10, 0, 270, 240, 10900, 25200, 551950, 2116800, 32458860, 169092000, 2120787900, 13427013600, 149506414200, 1075081207200, 11143223412750, 87198375264000, 865743970019500, 7171730187336000, 69416724049550020

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

Cf. A002898.

Sequence in context: A089831 A221414 A326719 * A216797 A221305 A173775

Adjacent sequences: A070187 A070188 A070189 * A070191 A070192 A070193

Keyword

nonn

Author

Karol A. Penson, Apr 26 2002

Status

approved