A126725 a(1)=0, a(2)=1; for n>2, a(n) = C(n,2)*(1+a(n-2)).

0, 1, 3, 12, 40, 195, 861, 5488, 31032, 247005, 1706815, 16302396, 133131648, 1483518127, 13978823145, 178022175360, 1901119947856, 27237392830233, 325091511083547, 5175104637744460, 68269217327545080, 1195449171318970491

Offset: 1

Author

Allan L. Edmonds (edmonds(AT)indiana.edu), Feb 13 2007

Keywords

• nonn

Comments

a(n) is also the maximum number of ways to place node pairs in an area formed by n 1 X 1 squares. - Theodore M. Mishura, Mar 20 2015

Crossrefs

Cf. A087214.

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else Binomial(n,2)*(1+Self(n-2)): n in [1..35]]; // Vincenzo Librandi, Mar 17 2015

Maple

seq(simplify(hypergeom([1, 1-n/2, 3/2-n/2], [], 2))*(n-1)*n/2,n=1..22);  # Mark van Hoeij, May 12 2013

Mathematica

nxt[{n_,a_,b_}]:={n+1,b,Binomial[n+1,2](a+1)}; Transpose[NestList[nxt,{2,0,1},30]][[2]] (* Harvey P. Dale, Oct 12 2014 *)

Formula

a(n) = A087214(n) - 1. - N. J. A. Sloane, Feb 15 2007

a(n) = Sum_{k=1..floor(n/2)} 2^k*Pochhammer(-n/2,k)*Pochhammer(1/2-n/2,k). - Theodore M. Mishura, Mar 16 2015

a(n) ~ n! * (exp(sqrt(2)) + (-1)^n * exp(-sqrt(2))) / 2^(n/2+1). - Vaclav Kotesovec, Mar 20 2015

Extensions

Edited by Vladeta Jovovic, Feb 20 2009