A127777 A127773 * A002260 as infinite lower triangular matrices.

1, 3, 6, 6, 12, 18, 10, 20, 30, 40, 15, 30, 45, 60, 75, 21, 42, 63, 84, 105, 126, 28, 56, 84, 112, 140, 168, 196, 36, 72, 108, 144, 180, 216, 252, 288, 45, 90, 135, 180, 225, 270, 315, 360, 405, 55, 110, 165, 220, 275, 330, 385, 440, 495, 550, 66, 132, 198

Offset

1,2

Comments

Triangular number transform of A002260.

Swapped order of the factors: A002260 * A127773 = A127778.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

T(n,k) = k*binomial(n+1,n-1) = Sum_{i=1..k} i*binomial(k,i)*binomial(n+2-k,n-i), 1 <= k <= n. - Mircea Merca, Apr 11 2012

Example

First few rows of the triangle:
   1;
   3,  6;
   6, 12, 18;
  10, 20, 30, 40;
  15, 30, 45, 60, 75;
  ...

Maple

T(n, k):=piecewise(k<=n, k*binomial(n+1, n-1), n<k, 0) # Mircea Merca, Apr 11 2012

Mathematica

Table[k*Binomial[n+1, n-1], {n, 20}, {k, n}]//Flatten (* Harvey P. Dale, Oct 26 2016 *)

Crossrefs

Cf. A000217, A127773, A000537 (row sums), A127778.

Sequence in context: A080866 A310131 A066393 * A307204 A208445 A208796

Adjacent sequences: A127774 A127775 A127776 * A127778 A127779 A127780

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jan 28 2007

Extensions

More terms from Harvey P. Dale, Oct 26 2016

Status

approved