This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A073410 Number of permutations p of (1,2,3,...,n) such that 1*(-1)^p(1)+2*(-1)^p(2)+3*(-1)^p(3)+...+n*(-1)^p(n)=0. 2
 1, 0, 0, 2, 8, 0, 0, 576, 4608, 0, 0, 2505600, 30067200, 0, 0, 53444966400, 855119462400, 0, 0, 3587014803456000, 71740296069120000, 0, 0, 584198928937451520000, 14020774294498836480000, 0, 0, 196340349691596912721920000, 5497529791364713556213760000, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Equivalently the number of grand Dyck n-paths in which each run length is selected from {1..2*n} without replacement. - David Scambler, Apr 16 2013 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA It seems that a(n)=0 if n==1 or 2 (mod 4) and a(4*k)=4*k*a(4*k-1). - Benoit Cloitre, Aug 23 2002 MAPLE b:= proc(n, i, c) option remember; `if`(abs(n)>i*(i+1)/2, 0,       `if`(i=0, `if`(abs(c)<2, 1, 0),        b(n+i, i-1, c+1) +b(n-i, i-1, c-1)))     end: a:= n-> b(0, n, 0)*floor(n/2)!*ceil(n/2)!/2^irem(n, 2): seq(a(n), n=0..40);  # Alois P. Heinz, Apr 29 2015 MATHEMATICA b[n_, i_, c_] := b[n, i, c] = If[Abs[n] > i*(i+1)/2, 0, If[i == 0, If[Abs[c]<2, 1, 0], b[n+i, i-1, c+1] + b[n-i, i-1, c-1]]]; a[n_] := b[0, n, 0]*Floor[n/2]! *Ceiling[n/2]!/2^Mod[n, 2]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 12 2015, after Alois P. Heinz *) PROG (PARI) a(n)=sum(k=1, n!, if(sum(i=1, n, i*(-1)^component(numtoperm(n, k), i)), 0, 1)) CROSSREFS Cf. A227850. Sequence in context: A230915 A242922 A242530 * A021361 A199156 A073001 Adjacent sequences:  A073407 A073408 A073409 * A073411 A073412 A073413 KEYWORD nonn AUTHOR Benoit Cloitre, Aug 23 2002 EXTENSIONS More terms from John W. Layman, Feb 05 2003 a(14)-a(22) from Robert Gerbicz, Nov 22 2010 a(0), a(23)-a(30) from Alois P. Heinz, Apr 28 2015 STATUS approved

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

Last modified December 10 15:32 EST 2016. Contains 279003 sequences.