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Search: id:A004211
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| A004211 |
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Shifts one place left under 2nd order binomial transform.
(Formerly M2900)
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+0
6
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| 1, 1, 3, 11, 49, 257, 1539, 10299, 75905, 609441, 5284451, 49134923, 487026929, 5120905441, 56878092067, 664920021819, 8155340557697, 104652541401025, 1401572711758403, 19546873773314571, 283314887789276721
(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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Joerg Arndt, Fxtbook
N. J. A. Sloane, Transforms
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FORMULA
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E.g.f.: exp(sinh(x)*exp(x)). O.g.f. A(x) satisfies A'(x)/A(x) = e^(2x).
a_n=sum(2^(n-k)*stirling2(n, k), k=0..n). - Emeric Deutsch, Feb 11 2002
G.f.: sum{k>=0, x^k/prod[l=1..k, 1-2lx]}. - R. Stephan, Apr 18 2004
Stirling transform of A000085. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 14 2004
O.g.f.: A(x) = 1/(1-x-2*x^2/(1-3*x-4*x^2/(1-5*x-6*x^2/(1-... -(2*n-1)*x-2*n*x^2/(1- ...))))) (continued fraction). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 17 2006
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}*2^{n-1}*f_n(1/2). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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MATHEMATICA
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Table[ Sum[ StirlingS2[ n, k ] 2^(-k+n), {k, n} ], {n, 16} ] (Wouter L. J. MEEUSSEN)
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CROSSREFS
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Cf. A075497 (row sums).
Sequence in context: A095822 A025539 A074528 this_sequence A001339 A012316 A058733
Adjacent sequences: A004208 A004209 A004210 this_sequence A004212 A004213 A004214
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KEYWORD
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nonn,easy,nice,eigen
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AUTHOR
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njas
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