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A129825
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n!*Bernoulli(n-1), n>2.
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9
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0, 1, 1, 1, 0, -4, 0, 120, 0, -12096, 0, 3024000, 0, -1576143360, 0, 1525620096000, 0, -2522591034163200, 0, 6686974460694528000, 0, -27033456071346536448000, 0, 160078872315904478576640000, 0, -1342964491649083924630732800000, 0, 15522270327163593186886877184000000, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Define "conjugated" Bernoulli numbers G(n) via G(0)=0, G(1)=B(0)=1, G(2)=-B(1)=1/2, G(n+1)=B(n), where B(n)=A027641(n)/A027642(n).
The sequence is then defined by a(n)=n!*G(n).
The first differences are 1, 0, 0, -1, -4, 4, 120, -120, -12096,...
The 2nd differences are -1, 0, -1, -3, 8, 116, -240, -11976, 24192, 3011904,...
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 18 2009: (Start)
a(n) = sum( (-1)^(k+1)*(n!/k)*S2(n, k)*(k-1)!, k=1..n).
a(n) = sum(((-1)^k/((k)!*(k+1)!))*(n!)*A028246(n, k+1)*A008955(k, k), k = 0..n-1).
(End)
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MAPLE
| A129825 := proc(n) if n <= 1 then n; elif n = 2 then 1; else n!*bernoulli(n-1) ; fi; end: # R. J. Mathar, May 21 2009
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CROSSREFS
| Cf. A129716, A129826.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 18 2009: (Start)
Equals second left hand column of A161739 (RSEG2 triangle).
Other left hand columns are A161742 and A161743.
Cf. A094310 [T(n,k) = n!/k], A008277 [S2(n,k); Stirling numbers of the second kind], A028246 [Worpitzky's triangle] and A008955 [CFN triangle].
(End)
Sequence in context: A118440 A013037 A129814 * A138734 A119010 A176050
Adjacent sequences: A129822 A129823 A129824 * A129826 A129827 A129828
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KEYWORD
| sign
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jun 03 2007
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 21 2009
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