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

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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..10.

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 *)

Prog

(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]

Crossrefs

Cf. A135950, A022166.

Sequence in context: A277413 A210920 A140048 * A361254 A093245 A108231

Adjacent sequences: A135948 A135949 A135950 * A135952 A135953 A135954

Keyword

sign

Author

Paul D. Hanna, Dec 08 2007

Status

approved