Search: id:A005727
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%I A005727 M0868
%S A005727 1,1,2,3,8,10,54,42,944,5112,47160,419760,4297512,47607144,575023344,
%T A005727 7500202920,105180931200,1578296510400,25238664189504,428528786243904,
%U A005727 7700297625889920,146004847062359040,2913398154375730560
%V A005727 1,1,2,3,8,10,54,-42,944,-5112,47160,-419760,4297512,-47607144,575023344,
%W A005727 -7500202920,105180931200,-1578296510400,25238664189504,-428528786243904,
%X A005727 7700297625889920,-146004847062359040,2913398154375730560
%N A005727 n-th derivative of x^x at x=1. Also called Lehmer-Comtet numbers.
%D A005727 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 139, table at foot 
               of page.
%D A005727 H. W. Gould, Rocky Mountain J. Math. 26(2) 1996.
%D A005727 R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), 
               no. 8, 697-712.
%D A005727 D. H. Lehmer, Numbers associated with Stirling Numbers and x^x, Rocky 
               Mountain J. Math., 15(2) 1985, p. 461.
%D A005727 G. H. Hardy, A Course of Pure Mathematics, 10th ed., Cambridge University 
               Press, 1960, p. 428.
%D A005727 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005727 T. D. Noe, <a href="b005727.txt">Table of n, a(n) for n=0..100</a>
%H A005727 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A005727 G. H. Hardy, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=b88432273f115fb346725f1a42422e19;
               c=umhistmath;idno=ACM1516.0001.001">A Course of Pure Mathematics</
               a>, Cambridge, The University Press, 1908.
%F A005727 For n>0, a(n)=sum(b(n, k), k=0..n), where b(n, k) is a Lehmer-Comtet 
               number of the first kind (see A008296).
%F A005727 E.g.f.: (1+x)^(1+x). a(n) = Sum_{k=0..n} Stirling1(n, k)*A000248(k). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 02 2003
%t A005727 NestList[ Factor[ D[ #1, x ] ]&, x^x, n ] /. (x->1)
%o A005727 (PARI) a(n)=if(n<0,0,n!*polcoeff((1+x+x*O(x^n))^(1+x),n))
%Y A005727 Cf. A005168. Row sums of A008296.
%Y A005727 Sequence in context: A165153 A121989 A010786 this_sequence A118089 A084917 
               A134713
%Y A005727 Adjacent sequences: A005724 A005725 A005726 this_sequence A005728 A005729 
               A005730
%K A005727 sign,easy,nice
%O A005727 0,3
%A A005727 N. J. A. Sloane (njas(AT)research.att.com).

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