%I A001569 M2161 N0861
%S A001569 1,1,1,2,37,329,1501,31354,1451967,39284461,737652869,560823394,1103386777549,
%T A001569 82520245792997,4398448305245905,168910341581721494,998428794798272641,
%U A001569 720450682719825322809,105099789680808769094057,10594247095804692725600734
%V A001569 1,-1,-1,2,37,329,1501,-31354,-1451967,-39284461,-737652869,560823394,
               1103386777549,
%W A001569 82520245792997,4398448305245905,168910341581721494,998428794798272641,
%X A001569 -720450682719825322809,-105099789680808769094057,-10594247095804692725600734
%N A001569 Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0,2*(1-exp(x))^(1/2)).
%D A001569 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001569 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001569 S. M. Kerawala, Asymptotic solution of the "Probleme des menages", Bull. 
               Calcutta Math. Soc., 39 (1947), 82-84.
%F A001569 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).
%F A001569 a(n) = n!*Sum_{k=0..n} (-1)^k*Stirling2(n,k)/k!. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jul 17 2006
%Y A001569 Sequence in context: A139119 A053788 A078976 this_sequence A092853 A100849 
               A120047
%Y A001569 Adjacent sequences: A001566 A001567 A001568 this_sequence A001570 A001571 
               A001572
%K A001569 sign,easy
%O A001569 0,4
%A A001569 N. J. A. Sloane (njas(AT)research.att.com).
%E A001569 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 17 2006