

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
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OFFSET

0,4


COMMENTS

Coefficient of the e^(2x) term in the numerator of the nth derivative of 1/(2e^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/((12*x)^2*(14*x)).
a(n) = Sum_{k=0..n} (1)^k*3^(nk)*binomial(n, k)*floor(k/2). (End)
a(n) = 4^(n1)  (n+1)*2^(n2).  Bruno Petazzoni (bruno(AT)enix.org), Apr 18 2007
a(n+1) = Sum_{k=0..n} k*2^(2*n1k).  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^(n1)(n+1)*2^(n2): n in [0..30]]; // Vincenzo Librandi, Jul 18 2019
(Sage) [2^(n2)*(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



