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A126390
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a(n) = Sum_{i=0..n} 2^i*B(i)*binomial(n,i) where B(n) = Bell numbers A000110(n).
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4
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1, 3, 13, 71, 457, 3355, 27509, 248127, 2434129, 25741939, 291397789, 3510328695, 44782460313, 602513988107, 8518757813637, 126179029108463, 1952609274344353, 31492811964616163, 528249539951292461, 9197240228562763687, 165923214676585626729
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Toufik Mansour and Mark Shattuck, A RECURRENCE RELATED TO THE BELL NUMBERS, INTEGERS 11 (2011), #A67; http://www.emis.de/journals/INTEGERS/papers/l67/l67.pdf.
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FORMULA
| E.g.f.: exp(exp(2*x)-1+x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 04 2007
a(n) = e^(-1)* (2)^n * sum( (k+1/2)^n / k!, k=0..infinity ). This is a Dobinski-type formula. - Karol A. Penson (penson(AT)lptl.jussieu.fr) and Olivier Gerard, Oct 22 2007
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MAPLE
| with(combstruct):seq(count(([S, {N=Union(Z, S, P), S=Set(Union(Z, P), card>=0), P=Set(Union(Z, Z), card>=1)}, labeled], size=n)), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 18 2008
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MATHEMATICA
| Table[ Sum[ (2)^(k) Binomial[n, k] BellB[k], {k, 0, n}], {n, 0, 30}] - Karol A. Penson (penson(AT)lptl.jussieu.fr) and Olivier Gerard, Oct 22 2007
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CROSSREFS
| Cf. A000110, A000296, A005493, A124311, A126617.
Sequence in context: A198447 A162326 A122455 * A167894 A003319 A158882
Adjacent sequences: A126387 A126388 A126389 * A126391 A126392 A126393
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 04 2007
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