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Search: id:A004212
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| A004212 |
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Shifts one place left under 3rd order binomial transform.
(Formerly M3557)
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+0
2
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| 1, 1, 4, 19, 109, 742, 5815, 51193, 498118, 5296321, 60987817, 754940848, 9983845261, 140329768789, 2087182244308, 32725315072135, 539118388883449, 9304591246975030, 167804098493079547, 3155000165773280893
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals the eigensequence of triangle A027465, the cube of Pascal's triangle. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 10 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Kerber, A matrix of combinatorial numbers related to the symmetric groups, Discrete Math., 21 (1978), 319-321.
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LINKS
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Joerg Arndt, Fxtbook
N. J. A. Sloane, Transforms
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FORMULA
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a_n=sum(3^(n-k)*stirling2(n, k), k=0..n). - Emeric Deutsch, Feb 11, 2002
E.g.f.: exp((exp(3*x)-1)/3). O.g.f. A(x) satisfies A'(x)/A(x) = e^(3*x).
Hankel transform is A000178(n)*3^C(n+1,2). - Paul Barry (pbarry(AT)wit.ie), Mar 31 2008
Define f_1(x),f_2(x),... such that f_1(x)=e^x, f_{n+1}(x)=diff(x*f_n(x),x), for n=2,3,.... Then a(n)=e^{-1/2}*3^{n-1}*f_n(1/3). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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CROSSREFS
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Cf. A075498 (row sums).
A027465 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 10 2009]
Sequence in context: A052751 A091643 A117397 this_sequence A060905 A127548 A122835
Adjacent sequences: A004209 A004210 A004211 this_sequence A004213 A004214 A004215
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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