A135951 Central terms of triangle A135950, the matrix inverse of triangle A022166.

1, -3, 70, -11160, 12850368, -111842970624, 7558738517524480, -4024873276683363287040, 17013427111087951089139449856, -573105858480900876266937950612226048, 154142404695090288939416498797330749299097600

Offset: 0

Author

Paul D. Hanna, Dec 08 2007

Keywords

• sign

Comments

A022166 is the triangle of Gaussian binomial coefficients [n,k] for q = 2.

Crossrefs

Cf. A135950, A022166.

Programs

Mathematica

max = 20; M = Table[QBinomial[n, k, 2], {n, 0, max}, {k, 0, max}] // Inverse; Table[M[[n, (n+1)/2]], {n, 1, max+1, 2}] (* Jean-François Alcover, Apr 09 2016 *)
Table[(-1)^n 2^((n-1)n/2) QBinomial[2n, n, 2], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)

PARI

a(n)=local(q=2,A=matrix(2*n+1,2*n+1,n,k,if(n>=k,if(n==1 || k==1, 1, prod(j=n-k+1, n-1, 1-q^j)/prod(j=1, k-1, 1-q^j))))^-1);A[2*n+1,n+1]