Search: id:A002119
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%I A002119 M4444 N1880
%S A002119 1,1,7,71,1001,18089,398959,10391023,312129649,10622799089,403978495031,
%T A002119 16977719590391,781379079653017,39085931702241241,2111421691000680031,
%U A002119 122501544009741683039,7597207150294985028449,501538173463478753560673
%V A002119 1,-1,7,-71,1001,-18089,398959,-10391023,312129649,-10622799089,403978495031,
%W A002119 -16977719590391,781379079653017,-39085931702241241,2111421691000680031,
%X A002119 -122501544009741683039,7597207150294985028449,-501538173463478753560673
%N A002119 Bessel polynomial y_n(-2).
%C A002119 Absolute values give denominators of successive convergents to e using 
               continued fraction 1+2/(1+1/(6+1/(10+1/(14+1/(18+1/(22+1/26...)))))).
%D A002119 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002119 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002119 Leo Chao, Paul DesJarlais and John L Leonard, A binomial identity, via 
               derangements, Math. Gaz. 89 (2005), 268-270..
%D A002119 L. Euler, 1737.
%D A002119 J. W. L. Glaisher, Reports of British Assoc. Adv. Sci., 1871, pp. 16-18.
%D A002119 D. H. Lehmer, Review of various tables by P. Pederson, Math. Comp., 2 
               (1946), 68-69.
%D A002119 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
%H A002119 T. D. Noe, <a href="b002119.txt">Table of n, a(n) for n=0..100</a>
%H A002119 <a href="Sindx_Be.html#Bessel">Index entries for sequences related to 
               Bessel functions or polynomials</a>
%F A002119 a(n) = -2(2n-1)*a(n-1) + a(n-2). - T. D. Noe, Oct 26 2006
%F A002119 If y = x + Sum_{k>1} A005363(k)*x^k/k!, then y = x + Sum{k>1} a(k-2)(-y)^k/
               k!. - Michael Somos Apr 02 2007
%F A002119 a(-n-1)= a(n). - Michael Somos Apr 02 2007
%o A002119 (PARI) {a(n)= if(n<0, n=-n-1); sum(k=0, n, (2*n-k)!/ (k!*(n-k)!)* (-1)^(n-k) 
               )} /* Michael Somos Apr 02 2007 */
%o A002119 (PARI) {a(n)= local(A); if(n<0, n= -n-1); A= sqrt(1 +4*x +x*O(x^n)); 
               n!*polcoeff( exp((A-1)/2)/A, n)} /* Michael Somos Apr 02 2007 */
%o A002119 (PARI) {a(n)= local(A); if(n<0, n= -n-1); n+=2 ; for(k= 1, n, A+= x*O(x^k); 
               A= truncate( (1+x)* exp(A) -1-A) ); A+= x*O(x^n); A-= A^2; -(-1)^n*n!* 
               polcoeff( serreverse(A), n)} /* Michael Somos Apr 02 2007 */
%Y A002119 Cf. A001517, A053556, A053557, A001514, A065920, A065921, A065922, A065707, 
               A000806, A006199, A065923.
%Y A002119 See also A033815.
%Y A002119 Polynomial coefficients are in A001498.
%Y A002119 Sequence in context: A048552 A067307 A052390 this_sequence A146752 A022518 
               A113053
%Y A002119 Adjacent sequences: A002116 A002117 A002118 this_sequence A002120 A002121 
               A002122
%K A002119 sign,easy,nice
%O A002119 0,3
%A A002119 N. J. A. Sloane (njas(AT)research.att.com).
%E A002119 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 03 2000

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