A195422 Permanents of certain n X 2 cyclic (1,-1) matrices.

-3, 2, 2, -8, 16, -16, 80, 384, 4160, 43008, 494336, 6136832, 82118656, 1178294272, 18053433344, 294241402880, 5083946115072, 92835116318720, 1786595439869952, 36144509314138112, 766933328068345856

Offset

1,1

Links

Table of n, a(n) for n=1..21.

A. R. Krauter, Uber die Permanente gewisser Matrizen und damit zusammenhangender..., Sem. Loth. Combinat. B11B (1984) 82-94, eq. (3.12)

Formula

a(n) = Sum_{k=0..n} (-2)^k*2*n*binomial(2*n-k,k)*(n-k)!/(2*n-k).

a(n) ~ exp(-4) * n!. - Vaclav Kotesovec, Dec 17 2015

Conjecture: (-n+2)*a(n) +(n^2-4*n+6)*a(n-1) +2*(n^2-2*n+3)*a(n-2) +8*(n-1)*a(n-3) = 0. - R. J. Mathar, Jul 20 2016

Conjecture: a(n) -n*a(n-1) -8*a(n-2) +4*(n-4)*a(n-3) +16*a(n-4) = 0. - R. J. Mathar, Jul 20 2016

Maple

A195422 := proc(n)
    local k;
    add((-2)^k*2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), k=0..n) ;
end proc: # R. J. Mathar, Jul 20 2016

Mathematica

Table[Sum[(-2)^k*2*n*Binomial[2*n - k, k]*(n - k)!/(2*n - k), {k, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Dec 17 2015 *)

Crossrefs

Sequence in context: A242703 A141456 A137445 * A176530 A011319 A177460

Adjacent sequences: A195419 A195420 A195421 * A195423 A195424 A195425

Keyword

sign,easy

Author

R. J. Mathar, Sep 18 2011

Status

approved