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Search: id:A005011
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| A005011 |
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Shifts one place left under 5th order binomial transform.
(Formerly M4240)
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+0
2
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| 1, 1, 6, 41, 331, 3176, 35451, 447981, 6282416, 96546231, 1611270851, 28985293526, 558413253581, 11458179765541, 249255304141006, 5725640423174901, 138407987170952351, 3510263847256823056
(list; graph; listen)
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OFFSET
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0,3
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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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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
N. J. A. Sloane, Transforms
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FORMULA
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a(n)=sum((5^(n-m))*stirling2(n, m), m=0..n), n>=0.
E.g.f.: exp((exp(5*x)-1)/5). O.g.f. A(x) satisfies A'(x)/A(x) = exp(5*x).
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^{-1/5}*5^{n-1}*f_n(1/5). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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CROSSREFS
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Cf. A075500 (row sums).
Sequence in context: A024078 A095177 A083430 this_sequence A009122 A094869 A006198
Adjacent sequences: A005008 A005009 A005010 this_sequence A005012 A005013 A005014
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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