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A091346
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Binomial convolution of A069321(n), where A069321(0)=0, with the sequence of all ones alternating in sign.
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1
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0, 1, 3, 19, 135, 1171, 11823, 136459, 1771815, 25561891, 405658143, 7022891899, 131714587095, 2660335742611, 57570797744463, 1328913670495339, 32592691757283975, 846383665814211331, 23200396829832102783
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=Sum(C(n, k)(-1)^(n-k)Sum(i!i Stirling2(k, i), i=1, .., k), k=0, .., n). E.g.f.: ((exp(x)-1)/(2-exp(x))^2)*exp(-x)
a(n) = (A000670(n+1)+(-1)^(n+1))/4. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 17 2005
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MATHEMATICA
| Table[Sum[Binomial[n, k](-1)^(n-k)Sum[i!i StirlingS2[k, i], {i, 1, k}], {k, 0, n}], {n, 0, 20}]
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CROSSREFS
| Cf. A083410.
Sequence in context: A199484 A063395 A074567 * A035086 A105797 A138513
Adjacent sequences: A091343 A091344 A091345 * A091347 A091348 A091349
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Jan 02 2004
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