The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A100575 Half the number of permutations of 0..n with exactly two maxima. 9
 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; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-20,16). FORMULA From Paul Barry, Jan 28 2005: (Start) G.f.: x^2/((1-2*x)^2*(1-4*x)). a(n) = Sum_{k=0..n} (-1)^k*3^(n-k)*binomial(n, k)*floor(k/2). (End) a(n) = 4^(n-1) - (n+1)*2^(n-2). - Bruno Petazzoni (bruno(AT)enix.org), Apr 18 2007 a(n+1) = Sum_{k=0..n} k*2^(2*n-1-k). - Philippe Deléham , Oct 29 2013 E.g.f.: (1/4)*(exp(4*x) - (1 + 2*x)*exp(2*x)). - G. C. Greubel, Mar 21 2022 EXAMPLE a(2)=1 because there are two maxima in 2,0,1 and 1,0,2 MATHEMATICA 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, Dec 01 2004 *) LinearRecurrence[{8, -20, 16}, {0, 0, 1}, 30] (* Harvey P. Dale, Apr 21 2020 *) PROG (Magma) [4^(n-1)-(n+1)*2^(n-2): n in [0..30]]; // Vincenzo Librandi, Jul 18 2019 (Sage) [2^(n-2)*(2^n -(n+1)) for n in (0..30)] # G. C. Greubel, Mar 21 2022 CROSSREFS Cf. A000431. Sequence in context: A273639 A022636 A003518 * A272112 A271005 A003220 Adjacent sequences: A100572 A100573 A100574 * A100576 A100577 A100578 KEYWORD nonn AUTHOR Anthony C Robin, Nov 29 2004 EXTENSIONS Edited by Robert G. Wilson v, Dec 01 2004 Definition corrected by Bruno Petazzoni (bruno(AT)enix.org), Apr 13 2007 New and simpler definition from R. H. Hardin, Aug 09 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 01:43 EST 2022. Contains 358572 sequences. (Running on oeis4.)