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Search: id:A100575
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| A100575 |
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Half the number of permutations of 0..n with exactly two maxima. |
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+0
7
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| 0, 0, 1, 8, 44, 208, 912, 3840, 15808, 64256, 259328, 1042432, 4180992, 16748544, 67047424, 268304384, 1073463296, 4294377472, 17178624000, 68716855296, 274872401920, 1099500093440, 4398022393856, 17592135712768, 70368639320064
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Coefficient of the e^(2x) term in the numerator of the n-th derivative of 1/(2-e^x).
This sequence, multiplied by 8, appears in a combinatorial problem about DNA chips. - Bruno Petazzoni (bruno(AT)enix.org), Apr 18 2007
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FORMULA
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G.f.: x^2/((1-2x)^2(1-4x)); a(n)=sum{k=0..n, (-1)^k*3^(n-k)*binomial(n, k)floor(k/2)}. - Paul Barry (pbarry(AT)wit.ie), Jan 28 2005
a(n) = 4^(n-1) - (n+1)*2^(n-2). - Bruno Petazzoni (bruno(AT)enix.org), Apr 18 2007
(1/4) [4^n - (n+1)*2^n ]. - Ralf Stephan, May 15 2007
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EXAMPLE
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a(2)=1 because there are two maxima in 2,0,1 and 1,0,2
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MATHEMATICA
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d = Drop[ Flatten[ CoefficientList[ Table[ Simplify[ D[1/(2 - E^x), {x, n}]*(E^x - 2)^(n + 1)/E^x], {n, 2, 24}], E^x]], 1]; a = {}; Do[AppendTo[a, Abs[d[[n(n + 1)/2]]]], {n, 23}]; a (Robert G. Wilson v)
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CROSSREFS
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Adjacent sequences: A100572 A100573 A100574 this_sequence A100576 A100577 A100578
Sequence in context: A073380 A022636 A003518 this_sequence A003220 A125318 A000373
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KEYWORD
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nonn
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AUTHOR
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Anthony C Robin (anthony_robin(AT)hotmail.com), Nov 29 2004
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 01 2004
Definition corrected by Bruno Petazzoni (bruno(AT)enix.org), Apr 13 2007
New and simpler definition from Ron Hardin (rhh(AT)cadence.com), Aug 09 2007
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