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A003659
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Shifts left under Stirling-2 transform.
(Formerly M1681)
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5
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1, 1, 2, 6, 26, 152, 1144, 10742, 122772, 1673856, 26780972, 496090330, 10519217930, 252851833482, 6832018188414, 205985750827854, 6885220780488694, 253685194149119818, 10250343686634687424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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 DELEHAM (kolotoko(AT)wanadoo.fr), Mar 23 2007
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REFERENCES
| 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]
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).
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LINKS
| M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
Istvan Mezo, On powers of Stirling matrices, Dec 21, 2008. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 22 2008]
N. J. A. Sloane, Transforms
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FORMULA
| E.g.f. A(x) satisfies A(x)'=1+A(exp(x)-1).
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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 */
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CROSSREFS
| Cf. A048801.
Cf. A153277, A153278. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 22 2008]
Sequence in context: A000629 A185994 A032187 * A159602 A032271 A205502
Adjacent sequences: A003656 A003657 A003658 * A003660 A003661 A003662
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KEYWORD
| nonn,nice,eigen
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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