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Search: id:A004213
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| A004213 |
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Shifts one place left under 4th order binomial transform.
(Formerly M3956)
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+0
2
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| 1, 1, 5, 29, 201, 1657, 15821, 170389, 2032785, 26546673, 376085653, 5736591885, 93614616409, 1625661357673, 29905322979421, 580513190237573, 11850869542405409, 253669139947767777, 5678266212792053029
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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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.
Joerg Arndt, Fxtbook
N. J. A. Sloane, Transforms
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FORMULA
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a(n)=sum((4^(n-m))*stirling2(n, m), m=0..n), n>=0.
E.g.f.: exp((exp(4*x)-1)/4). O.g.f. A(x) satisfies A'(x)/A(x) = e^(4x).
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^{-1/4}*4^{n-1}*f_n(1/4). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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CROSSREFS
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Cf. A075499 (row sums).
Adjacent sequences: A004210 A004211 A004212 this_sequence A004214 A004215 A004216
Sequence in context: A086672 A094710 A108453 this_sequence A105277 A103213 A057588
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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