A173988 Triangle T(n,k) = 2^(k-1)*n*binomial(n-k,2*k-2)/(n-3*k+3) if k<n/3+1, else T(n,k)=1.

1, 1, 1, 8, 1, 15, 1, 24, 1, 1, 35, 28, 1, 48, 80, 1, 1, 63, 180, 1, 1, 80, 350, 80, 1, 1, 99, 616, 308, 1, 1, 120, 1008, 896, 1, 1, 1, 143, 1560, 2184, 208, 1, 1, 168, 2310, 4704, 1008, 1, 1, 1, 195, 3300, 9240, 3600, 1, 1, 1, 224, 4576, 16896, 10560, 512, 1, 1, 1, 255, 6188, 29172

Offset

2,4

Comments

Row sums are 1, 1, 9, 16, 26, 64, 130, 245, 512, 1025, 2027,...

Links

Table of n, a(n) for n=2..69.

Example

The triangle starts in row n=2 with columns 1<= k <= n/2 as:
1;
1;
1, 8;
1, 15;
1, 24, 1;
1, 35, 28;
1, 48, 80, 1;
1, 63, 180, 1;
1, 80, 350, 80, 1;
1, 99, 616, 308, 1;
1, 120, 1008, 896, 1, 1;

Mathematica

g[n_, k_] = If[(n - 3*k + 3) > 0, 2^k*n*Binomial[n - k, 2*k - 2]/(n - 3*k + 3), 2]/2;
Table[Table[g[n, k], {k, 1, Floor[n/2]}], {n, 2, 12}];
Flatten[%]

Crossrefs

Sequence in context: A298143 A181762 A209684 * A349123 A158893 A342636

Adjacent sequences: A173985 A173986 A173987 * A173989 A173990 A173991

Keyword

nonn,easy,tabf

Author

Roger L. Bagula, Mar 04 2010

Extensions

Tabl replaced by tabf, replaced Mma notation, extended beyond n=12, removed broken link w/o author or title - The Assoc. Eds. of the OEIS - Nov 02 2010

Status

approved