A144480 T(n,k) = binomial(n, k)*min(k + 1, n - k + 1), triangle read by rows (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 18, 8, 1, 1, 10, 30, 30, 10, 1, 1, 12, 45, 80, 45, 12, 1, 1, 14, 63, 140, 140, 63, 14, 1, 1, 16, 84, 224, 350, 224, 84, 16, 1, 1, 18, 108, 336, 630, 630, 336, 108, 18, 1, 1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

If k <= floor(n/2), then T(n,k) = binomial(n, k)*(k + 1), otherwise T(n,k) = binomial(n, k)*(n - k - 1).

T(n,k) = A007318(n,k)*A003983(k+1,n-k+1), i.e., term-by term product of Pascal's triangle A007318 and A003983 as a triangle.

Example

Triangle begins:
  1;
  1,  1;
  1,  4,   1;
  1,  6,   6,   1;
  1,  8,  18,   8,    1;
  1, 10,  30,  30,   10,    1;
  1, 12,  45,  80,   45,   12,    1;
  1, 14,  63, 140,  140,   63,   14,   1;
  1, 16,  84, 224,  350,  224,   84,  16,   1;
  1, 18, 108, 336,  630,  630,  336, 108,  18,  1;
  1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1;
  ...

Mathematica

Table[Table[Binomial[n, m]*If[m <= Floor[n/2], 1 + m, 1 + n - m], {m, 0, n}], {n, 0, 10}] // Flatten

Prog

(Maxima) create_list(binomial(n, k)*min(k + 1, n - k + 1), n, 0, 10, k, 0, n); /* Franck Maminirina Ramaharo, Dec 10 2018 */

Crossrefs

Row sums are in A245560.

Cf. A003983, A007318, A168643.

Sequence in context: A141540 A143188 A102413 * A144463 A174376 A131399

Adjacent sequences: A144477 A144478 A144479 * A144481 A144482 A144483

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Oct 11 2008

Extensions

Entry revised by N. J. A. Sloane, Aug 07 2014

Edited by Franck Maminirina Ramaharo, Dec 10 2018

Status

approved