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A126617
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a(n) = Sum_{i=0..n} (-2)^(n-i)*B(i)*binomial(n,i) where B(n) = Bell numbers A000110(n).
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5
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1, -1, 2, -3, 7, -10, 31, -21, 204, 307, 2811, 12100, 74053, 432211, 2768858, 18473441, 129941283, 956187814, 7351696139, 58897405759, 490681196604, 4242903803727, 38014084430983, 352341755256348, 3373662303816313, 33326335433122711, 339232538387804530
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is positive starting at n=8. - Karol A. Penson (penson(AT)lptl.jussieu.fr) and Olivier Gerard, Oct 22 2007
Hankel transform is A000178. [From Paul Barry (pbarry(AT)wit.ie), Apr 23 2009]
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FORMULA
| E.g.f.: exp(exp(x)-2*x-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 04 2007
a(n) = e^(-1) * sum( (k-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
G.f.: 1/(1+x-x^2/(1-2x^2/(1-x-3x^2/(1-2x-4x^2/(1-3x-5x^2/(1-.... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Apr 23 2009]
Let A be the upper Hessenberg matrix of order n defined by: A[i,i-1]=-1, A[i,j]=binomial(j-1,i-1), (i<=j), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=(-1)^(n)charpoly(A,2). [From Milan R. Janjic (agnus(AT)blic.net), Jul 08 2010]
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MATHEMATICA
| Table[ Sum[ (-2)^(n - k) Binomial[n, k] BellB[k], {k, 0, n}], {n, 0, 50}] - Karol A. Penson (penson(AT)lptl.jussieu.fr) and Olivier Gerard, Oct 22 2007
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CROSSREFS
| Cf. A000110, A000296, A005493, A124311, A126390, A153732.
Sequence in context: A062113 A130968 A007748 * A117733 A066236 A118203
Adjacent sequences: A126614 A126615 A126616 * A126618 A126619 A126620
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 04 2007
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EXTENSIONS
| More terms from Karol A. Penson (penson(AT)lptl.jussieu.fr) and Olivier Gerard, Oct 22 2007
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