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A052749 2n*S2(n-1,2). 0
0, 0, 0, 6, 24, 70, 180, 434, 1008, 2286, 5100, 11242, 24552, 53222, 114660, 245730, 524256, 1114078, 2359260, 4980698, 10485720, 22020054, 46137300, 96468946, 201326544, 419430350, 872415180, 1811939274, 3758096328, 7784628166, 16106127300, 33285996482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..31.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 705

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

FORMULA

E.g.f.: exp(x)^2*x-2*x*exp(x)+x.

Recurrence: {a(1)=0, a(2)=0, a(3)=6, (2*n^2+6*n+4)*a(n)+(-6*n-3*n^2)*a(n+1)+(n^2+n)*a(n+2)}.

a(n) = Sum(n*2^(k-2), k=3..n). - Zerinvary Lajos, Oct 09 2006

a(n) = n*(2^(n-1)-2) = n*A000918(n-1), n>=3. - Mitch Harris, Oct 25 2006

O.g.f.: 2*x^3*(3-6*x+2*x^2)/((-1+x)^2*(-1+2*x)^2). - R. J. Mathar, Dec 05 2007

a(n) = sum_{j=1..n} ( sum_{i=2..n-1} (j+1)*2^(j-i-1) ). - Wesley Ivan Hurt, Nov 17 2014

a(n) = n*(2^n-4)/2, n>1. - Wesley Ivan Hurt, Nov 17 2014

a(n) = 2*A260006(n-2). - R. J. Mathar, Apr 26 2017

MAPLE

spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

g := taylor(exp(x)^2*x-2*x*exp(x)+x, x=0, 121): q := seq(coeff(g, x, i)*i!, i=0..120);

MATHEMATICA

Table[If[n < 3, 0, (n*(2^n - 3) - n)/2], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 30 2011 *)

LinearRecurrence[{6, -13, 12, -4}, {0, 0, 0, 6, 24, 70}, 40] (* Harvey P. Dale, Aug 30 2017 *)

PROG

(MAGMA) [n le 2 select 0 else n*(2^(n-1)-2): n in [0..40]]; // Vincenzo Librandi, Nov 18 2014

CROSSREFS

Sequence in context: A274772 A234271 A006528 * A262445 A090574 A294842

Adjacent sequences:  A052746 A052747 A052748 * A052750 A052751 A052752

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

Better description from Victor Adamchik (adamchik(AT)cs.cmu.edu), Jul 19 2001

STATUS

approved

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Last modified October 19 14:21 EDT 2018. Contains 316362 sequences. (Running on oeis4.)