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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

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