A156715 Let k=1; then T(n,m) = (((2*k+1)/(m+k+1))*binomial(n-1-k, m-k)*binomial(n+k, m+k) + ((2*k+1)/(n-m+k))*binomial(n-1-k, n-m-1-k)*binomial(n+k, n-m-1+k)), irregular triangle.

3, 3, 3, 12, 3, 3, 25, 25, 3, 3, 42, 90, 42, 3, 3, 63, 231, 231, 63, 3, 3, 88, 490, 840, 490, 88, 3, 3, 117, 918, 2394, 2394, 918, 117, 3, 3, 150, 1575, 5796, 8820, 5796, 1575, 150, 3, 3, 187, 2530, 12474, 26796, 26796, 12474, 2530, 187, 3

Offset

0,1

Links

Table of n, a(n) for n=0..53.

Example

{3, 3},
{3, 12, 3},
{3, 25, 25, 3},
{3, 42, 90, 42, 3},
{3, 63, 231, 231, 63, 3},
{3, 88, 490, 840, 490, 88, 3},
{3, 117, 918, 2394, 2394, 918, 117, 3},
{3, 150, 1575, 5796, 8820, 5796, 1575, 150, 3},
{3, 187, 2530, 12474, 26796, 26796, 12474, 2530, 187, 3}

Mathematica

With[{k = 1}, Table[(((2 k + 1)/(m + k + 1))*Binomial[n - 1 - k, m - k] * Binomial[n + k, m + k] + ((2 k + 1)/(n - m + k))*Binomial[n - 1 - k, n - m - 1 - k] * Binomial[n + k, n - m - 1 + k]), {n, k + 1, 10}, {m, 0, n - 1}]] // Flatten (* Michael De Vlieger, Dec 19 2022 *)

Crossrefs

Cf. A156716.

Sequence in context: A274993 A233202 A101480 * A133797 A225073 A152575

Adjacent sequences: A156712 A156713 A156714 * A156716 A156717 A156718

Keyword

nonn,tabf,less

Author

Roger L. Bagula, Feb 14 2009

Status

approved