A156716 Let k=2; 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.

5, 0, 5, 5, 15, 15, 5, 5, 35, 70, 35, 5, 5, 60, 210, 210, 60, 5, 5, 90, 486, 840, 486, 90, 5, 5, 125, 960, 2550, 2550, 960, 125, 5, 5, 165, 1705, 6435, 9900, 6435, 1705, 165, 5, 5, 210, 2805, 14245, 31185, 31185, 14245, 2805, 210, 5

Offset

3,1

Links

Table of n, a(n) for n=3..54.

Example

Triangle begins:
  5,   0,    5;
  5,  15,   15,     5;
  5,  35,   70,    35,     5;
  5,  60,  210,   210,    60,     5;
  5,  90,  486,   840,   486,    90,     5;
  5, 125,  960,  2550,  2550,   960,   125,    5;
  5, 165, 1705,  6435,  9900,  6435,  1705,  165,   5;
  5, 210, 2805, 14245, 31185, 31185, 14245, 2805, 210, 5;
   ...

Mathematica

With[{k = 2}, 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. A156715.

Sequence in context: A091672 A144702 A238192 * A055510 A200397 A265302

Adjacent sequences: A156713 A156714 A156715 * A156717 A156718 A156719

Keyword

nonn,tabf,less

Author

Roger L. Bagula, Feb 14 2009

Status

approved