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 A003659 Shifts left under Stirling-2 transform. (Formerly M1681) 8
 1, 1, 2, 6, 26, 152, 1144, 10742, 122772, 1673856, 26780972, 496090330, 10519217930, 252851833482, 6832018188414, 205985750827854, 6885220780488694, 253685194149119818, 10250343686634687424, 452108221967363310278, 21676762640915055856716 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Apart from leading term, number of M-sequences from multicomplexes on at most 4 variables with no monomial of degree more than n+1. Stirling-2 transform of a(n) = [1, 1, 2, 6, 26, ...] is a(n+1) = [1, 2, 6, 26, ...]. Eigensequence of Stirling-2 triangle A008277. - Philippe Deléham, Mar 23 2007 REFERENCES S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..330 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] M. Janjic, Determinants and Recurrence Sequences, Journal of Integer Sequences, 2012, Article 12.3.5. [N. J. A. Sloane, Sep 16 2012] Istvan Mezo, On powers of Stirling matrices, arXiv:0812.4047 [math.CO], 2008. [Jonathan Vos Post, Dec 22 2008] N. J. A. Sloane, Transforms FORMULA E.g.f. A(x) satisfies A(x)' = 1+A(exp(x)-1). G.f. satisfies: Sum_{n>=1} a(n)*x^n = x * (1 + Sum_{n>=1} a(n) * x^n / Product_{j=1..n} (1 - j*x)). - Ilya Gutkovskiy, May 09 2019 MAPLE stirtr:= proc(p)            proc(n) add(p(k)*Stirling2(n, k), k=0..n) end          end: a:= proc(n) option remember; `if`(n<3, 1, aa(n-1)) end: aa:= stirtr(a): seq(a(n), n=1..25);  # Alois P. Heinz, Jun 22 2012 MATHEMATICA terms = 21; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + A[Exp[x] - 1 + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x]*Range[0, terms]! // Rest (* Jean-François Alcover, May 23 2012, updated Jan 12 2018 *) PROG (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 */ CROSSREFS Cf. A048801. Cf. A153277, A153278. - Jonathan Vos Post, Dec 22 2008 Sequence in context: A000629 A185994 A032187 * A159602 A032271 A205502 Adjacent sequences:  A003656 A003657 A003658 * A003660 A003661 A003662 KEYWORD nonn,nice,eigen AUTHOR STATUS approved

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)