A141597 Triangle T(n,k) = 2*binomial(n,k)^2-1, read by rows, 0<=k<=n.

1, 1, 1, 1, 7, 1, 1, 17, 17, 1, 1, 31, 71, 31, 1, 1, 49, 199, 199, 49, 1, 1, 71, 449, 799, 449, 71, 1, 1, 97, 881, 2449, 2449, 881, 97, 1, 1, 127, 1567, 6271, 9799, 6271, 1567, 127, 1, 1, 161, 2591, 14111, 31751, 31751, 14111, 2591, 161, 1, 1, 199, 4049, 28799, 88199

Offset

0,5

Comments

Row sums are 1, 2, 9, 36, 135, 498, 1841, 6856, 25731, 97230, 369501,... = 2*binomial(2n,n)-(n+1) = A134759(n).

Links

Table of n, a(n) for n=0..59.

Example

1;
1, 1;
1, 7, 1;
1, 17, 17, 1;
1, 31, 71, 31, 1;
1, 49, 199, 199, 49, 1;
1, 71, 449, 799, 449, 71, 1;
1, 97, 881, 2449, 2449, 881, 97, 1;
1, 127, 1567, 6271, 9799, 6271, 1567, 127, 1;
1, 161, 2591, 14111, 31751, 31751, 14111, 2591, 161, 1;
1, 199, 4049, 28799, 88199, 127007, 88199, 28799, 4049, 199, 1;

Mathematica

Clear[t, n, m, k, l] t[n_, m_, k_, l_] := (1 + l)*Binomial[n, m]^k - l; k = 2; l = 1; Table[Table[t[n, m, k, l], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A141596.

Sequence in context: A081580 A082110 A275526 * A176561 A176284 A154233

Adjacent sequences: A141594 A141595 A141596 * A141598 A141599 A141600

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 21 2008

Status

approved