Search: id:A005121
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%I A005121 M3649
%S A005121 1,1,4,32,436,9012,262760,10270696,518277560,32795928016,2542945605432,
%T A005121 237106822506952,26173354092593696,3375693096567983232,
%U A005121 502995942483693043200,85750135569136650473360,16583651916595710735271248,
               3611157196483089769387182064,879518067472225603327860638128
%N A005121 Ultradissimilarity relations on an n-set.
%C A005121 First column in A154960. [From Mats Granvik (mats.granvik(AT)abo.fi), 
               Jan 18 2009]
%D A005121 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005121 L. Babai and T. Lengyel, A convergence criterion for recurrent sequences 
               with application to the partition lattice, Analysis 12 (1992), 109-119.
%D A005121 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 316-321.
%D A005121 T. Lengyel, On a recurrence involving Stirling numbers, Europ. J. Combin., 
               5 (1984), 313-321.
%D A005121 M. Schader, Hierarchical analysis: classification with ordinal object 
               dissimilarities, Metrika, 27 (1980), 127-132.
%H A005121 L. Babai and T. Lengyel, <a href="http://abacus.oxy.edu/papers/lengyel/
               analysis.ps">A convergence criterion for recurrent sequences with 
               application to the partition lattice</a>, Analysis 12 (1992), 109-119. 
               [Bad link]
%H A005121 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/lngy/lngy.html">
               Lengyel's Constant</a>
%H A005121 T. Prellberg, <a href="http://algo.inria.fr/seminars/sem02-03/prellberg1-slides.ps">
               On the asymptotic analysis of a class of linear recurrences</a> (slides).
%H A005121 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LengyelsConstant.html">Lengyel's Constant</a>
%F A005121 a(n)=Sum_{i=1..n-1} N_i(n), where N_k(m)=Sum_{j=k..m-1} Stirling2(m, 
               j)*N_{k-1}(j), m=3..n, k=2..m-1; N_1(2)=N_1(3)=...=N_1(n)=1.
%F A005121 a(n) = Sum_{k=1..n-1} Stirling2(n, k)*a(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Apr 16 2003
%F A005121 E.g.f. satisfies Z(z) = 1/2 * (Z(exp(z)-1) - z). (Lengyel)
%F A005121 Asymptotic growth: a(n) ~ C_L*(n!)^2*(2log(2))^(-n)*n^(-1-1/3*log(2)) 
               (Babai and Lengyel), with C_L = 1.0986858055... = A086053 (Flajolet 
               and Salvy).
%o A005121 (PARI) {a(n) = local(A); if( n<1, 0, for(k=1, n, A = truncate(A) + x*O(x^k); 
               A = x - A + subst(A, x, exp(x + x*O(x^k)) - 1)); n! * polcoeff(A, 
               n))} /* Michael Somos Sep 22 2007 */
%Y A005121 Cf. A006541. Row sums of A008826.
%Y A005121 Sequence in context: A140178 A088991 A009668 this_sequence A037964 A089285 
               A086906
%Y A005121 Adjacent sequences: A005118 A005119 A005120 this_sequence A005122 A005123 
               A005124
%K A005121 nonn,nice,easy
%O A005121 1,3
%A A005121 N. J. A. Sloane (njas(AT)research.att.com).
%E A005121 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 16 2003

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