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Search: id:A025168
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| A025168 |
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E.g.f.: exp(x/(1-2*x)). |
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+0
7
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| 1, 1, 5, 37, 361, 4361, 62701, 1044205, 19748177, 417787921, 9770678101, 250194150581, 6959638411705, 208919770666777, 6729933476435261, 231512615111396221, 8469125401589550241, 328241040596380393505, 13434223364220816489637, 578931271898150002093381
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela and A. I. Solomon, Hierarchical Dobinski-type relations via substitution and the moment problem [J. Phys. A 37 (2004), 3475-3487]
N. J. A. Sloane, Transforms
N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
Thomas Wieder, Expanded definitions of A103446 and A025168
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FORMULA
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Second LAH transform of A000012. LAH transform of A000262. a(n) = Sum_{k=0..n) 2^(n-k)*n!/k!*binomial(n-1, k-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 17 2003
Define f_1(x),f_2(x),... such that f_1(x)=e^x, f_{n+1}(x)=diff(x^2*f_n(x),x), for n=2,3,.... Then a(n)=e^{-1/2}*4*{n-1}*f_n(1/2). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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MAPLE
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with(combstruct); SetSeqSeqL := [T, {T=Set(S), S=Sequence(U, card >= 1), U=Sequence(Z, card >=1)}, labeled];
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MATHEMATICA
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Table[ n! 2^n LaguerreL[ n, 1, -1/2 ], {n, 0, 12} ]
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CROSSREFS
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Cf. A103446.
Sequence in context: A084212 A004208 A112698 this_sequence A084358 A050351 A129137
Adjacent sequences: A025165 A025166 A025167 this_sequence A025169 A025170 A025171
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KEYWORD
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nonn
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AUTHOR
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w.meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 08 2002
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