Search: id:A003659
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%I A003659 M1681
%S A003659 1,1,2,6,26,152,1144,10742,122772,1673856,26780972,496090330,
%T A003659 10519217930,252851833482,6832018188414,205985750827854,
%U A003659 6885220780488694,253685194149119818,10250343686634687424
%N A003659 Shifts left under Stirling-2 transform.
%C A003659 Apart from leading term, number of M-sequences from multicomplexes on 
               at most 4 variables with no monomial of degree more than n+1.
%C A003659 Stirling-2 transform of a(n) = [1, 1, 2, 6, 26, ...] is a(n+1) = [1, 
               2, 6, 26, ...].
%C A003659 Eigensequence of Stirling-2 triangle A008277. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 23 2007
%D A003659 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003659 S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 
               19 (1999), 255-266.
%D A003659 M. Bernstein, N. J. A. Sloane, Some canonical sequences of integers, 
               Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 
               210. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 22 2008]
%H A003659 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/
               0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 
               226-228 (1995), 57-72; erratum 320 (2000), 210.
%H A003659 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A003659 Istvan Mezo, <a href="http://arxiv.org/abs/0812.4047">On powers of Stirling 
               matrices</a>, Dec 21, 2008. [From Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Dec 22 2008]
%F A003659 E.g.f. A(x) satisfies A(x)'=1+A(exp(x)-1).
%o A003659 (PARI) {a(n)=local(A, E); if(n<0, 0, A=O(x); E=exp(x+x*O(x^n))-1; for(m=1, 
               n, A=intformal( subst( 1+A, x, E+x*O(x^m)))); n!*polcoeff(A, n))} 
               /* Michael Somos Mar 08 2004 */
%Y A003659 Cf. A048801.
%Y A003659 Cf. A153277, A153278. [From Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Dec 22 2008]
%Y A003659 Sequence in context: A159311 A000629 A032187 this_sequence A159602 A032271 
               A107104
%Y A003659 Adjacent sequences: A003656 A003657 A003658 this_sequence A003660 A003661 
               A003662
%K A003659 nonn,nice,eigen
%O A003659 1,3
%A A003659 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein

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