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A001569
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Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*(1-exp(x))^(1/2)).
(Formerly M2161 N0861)
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3
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1, -1, -1, 2, 37, 329, 1501, -31354, -1451967, -39284461, -737652869, 560823394, 1103386777549, 82520245792997, 4398448305245905, 168910341581721494, 998428794798272641, -720450682719825322809, -105099789680808769094057, -10594247095804692725600734
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| S. M. Kerawala, Asymptotic solution of the "Probleme des menages", Bull. Calcutta Math. Soc., 39 (1947), 82-84.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Let b(n) satisfy (n-2)*b(n)-n*(n-2)*b(n-1)-n*b(n-2)=0; write b(n)=(n!/e^2)*(1+sum a_r/n^r, r=1..inf).
a(n) = n!*Sum_{k=0..n} (-1)^k*Stirling2(n,k)/k!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 17 2006
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CROSSREFS
| Sequence in context: A053788 A078976 A200911 * A092853 A100849 A120047
Adjacent sequences: A001566 A001567 A001568 * A001570 A001571 A001572
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 17 2006
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