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A070190
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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.
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4
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1, 0, 10, 0, 270, 240, 10900, 25200, 551950, 2116800, 32458860, 169092000, 2120787900, 13427013600, 149506414200, 1075081207200, 11143223412750, 87198375264000, 865743970019500, 7171730187336000, 69416724049550020
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A002898.
Sequence in context: A089831 A221414 A326719 * A216797 A221305 A173775
Adjacent sequences: A070187 A070188 A070189 * A070191 A070192 A070193
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KEYWORD
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nonn
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AUTHOR
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Karol A. Penson, Apr 26 2002
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STATUS
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approved
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