A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)*A(j,i)*2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.

2, 1, 2, -1, 10, 6, 5, -35, 105, 30, -63, 420, -882, 1260, 210, 1576, -10395, 20790, -20790, 17325, 1890, -68409, 450450, -891891, 849420, -495495, 270270, 20790, 4729726, -31126095, 61486425, -57972915, 32207175, -12297285, 4729725, 270270

Offset

0,1

References

H. W. Gould, Power sum identities for arbitrary symmetric arrays, SIAM J. Appl. Math., 17 (1969), 307-316.

Links

Table of n, a(n) for n=0..35.

Example

Triangle begins:
2
1 2
-1 10 6
5 -35 105 30
-63 420 -882 1260 210

Crossrefs

Cf. A097474, A097801. Row sums give A001147. Is the left-hand edge A004193?

Sequence in context: A071559 A071560 A248516 * A126906 A179508 A134304

Adjacent sequences: A097746 A097747 A097748 * A097750 A097751 A097752

Keyword

sign,tabl,easy

Author

N. J. A. Sloane, Sep 21 2004

Extensions

More terms from Sean A. Irvine, Mar 25 2013

Status

approved