A178987 a(n) = n*(n-3)*2^(n-2).

0, -1, -2, 0, 16, 80, 288, 896, 2560, 6912, 17920, 45056, 110592, 266240, 630784, 1474560, 3407872, 7798784, 17694720, 39845888, 89128960, 198180864, 438304768, 964689920, 2113929216, 4613734400, 10032775168, 21743271936

Offset

0,3

Comments

Binomial transform of 0, -1 followed by A005563.

The sequence defines an array by adding higher order differences in successive rows:

0, -1, -2, 0, 16, 80, 288, 896, 2560, 6912, 17920, 45056, 110592, ...

-1, -1, 2, 16, 64, 208, 608, 1664, 4352, 11008, 27136, 65536, ... A127276

0, 3, 14, 48, 144, 400, 1056, 2688, 6656, 16128, 38400, 90112, 208896, ... A176027

3, 11, 34, 96, 256, 656, 1632, 3968, 9472, 22272, 51712, 118784, ... A084266

8, 23, 62, 160, 400, 976, 2336, 5504, 12800, 29440, 67072, ...

The left column of the array (binomial transform of the sequence) is A067998.

For n>2, the sequence gives the number of permutations in the symmetric group S_{n+1} with peaks exactly in positions 2 and n-1. See Theorem 10 in [Billey-Burdzy-Sagan] reference.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Sara Billey, Krzystof Burdzy and Bruce Sagan, Permutations With Given Peak Set, J. Integer Sequences, Vol. 16 (2013), online article 13.6.1.

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

a(n) = 16*A001793(n-3), n > 3.

a(n) = 8*A001788(n-2)-A052481(n-1). - R. J. Mathar, Jan 04 2011

a(n) = +6*a(n-1) -12*a(n-2) +8*a(n-3).

a(n+1)-a(n) = -A127276(n).

G.f.: -x*(-1+4*x)/(2*x-1)^3. - R. J. Mathar, Jan 04 2011

a(n) = Sum_{k=0..n-1} Sum_{i=0..n-1} (k-1) * C(n-1,i). - Wesley Ivan Hurt, Sep 20 2017

Mathematica

Table[n(n-3)2^(n-2), {n, 0, 30}] (* or *) LinearRecurrence[{6, -12, 8}, {0, -1, -2}, 30] (* Harvey P. Dale, Mar 24 2023 *)

Prog

(Magma) [n*(n-3)*2^(n-2): n in [0..30]]; // Vincenzo Librandi, Aug 04 2011

Crossrefs

Cf. A176027.

Sequence in context: A012661 A345652 A009528 * A242569 A152154 A324665

Adjacent sequences: A178984 A178985 A178986 * A178988 A178989 A178990

Keyword

sign,easy

Author

Paul Curtz, Jan 03 2011

Status

approved