A137783 a(n) = the number of permutations (p(1), p(2), ..., p(2n+1)) of (1, 2, ..., 2n+1) where, for each k (2 <= k <= 2n+1), the sign of (p(k) - p(k-1)) equals the sign of (p(2n+2-k) - p(2n+3-k)).

1, 4, 44, 1028, 40864, 2484032, 214050784, 24831582176, 3731039384576, 704879630525696, 163539441616948736, 45712130697710081024, 15150993151215400441856, 5875388829103413298173952, 2635427286694074346846232576, 1353918066433734600362650169344

Offset

0,2

Comments

There are no such permutations of (1,2,...,2n).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..90

Example

Consider the permutation (for n = 3): 3,4,5,2,7,6,1. The signs of the differences between adjacent terms form the sequence: ++-+--, which is the negative of its reversal. So this permutation, among others, is counted when n = 3.

Prog

(PARI) { a(n) = my(s, c, r); s=0; forvec(t=vector(n\2, i, [0, 2]), c=0; r=[]; for(j=1, #t, if(t[j]==0, c++, if(t[j]==1, r=concat(r, [j]), r=concat(r, [n-j])); ); ); r=vecsort(r); s+=(-2)^c*if(#r, n!/(r[1]!*prod(j=1, #r-1, (r[j+1]-r[j])!)*(n-r[ #r])!), 1) ); s } /* Max Alekseyev */

Crossrefs

Cf. A060350, A137782.

Sequence in context: A301942 A348130 A255928 * A136552 A155556 A188456

Adjacent sequences: A137780 A137781 A137782 * A137784 A137785 A137786

Keyword

nonn

Author

Leroy Quet, Feb 10 2008, Feb 14 2008

Extensions

First 4 terms calculated by Olivier Gérard

Edited and extended by Max Alekseyev, May 09 2009

Status

approved