A134399 Matrix product of Binomial triangle A007318 and triangle with (1, 1, 2, 3, 4, 5, ...) in the main diagonal and the rest zeros.

1, 1, 1, 1, 2, 2, 1, 3, 6, 3, 1, 4, 12, 12, 4, 1, 5, 20, 30, 20, 5, 1, 6, 30, 60, 60, 30, 6, 1, 7, 42, 105, 140, 105, 42, 7, 1, 8, 56, 168, 280, 280, 168, 56, 8, 1, 9, 72, 252, 504, 630, 504, 252, 72, 9

Offset

0,5

Comments

Row sums = A005183: (1, 2, 5, 13, 33, 81, 193, ...).

Links

Table of n, a(n) for n=0..54.

Formula

T(n,0) = 1; T(n,k) = k*binomial(n,k) for 1 <= k <= n. [corrected by Paolo Xausa, May 03 2024]

Example

First few rows of the triangle:
  1;
  1, 1;
  1, 2,  2;
  1, 3,  6,   3;
  1, 4, 12,  12,   4;
  1, 5, 20,  30,  20,   5;
  1, 6, 30,  60,  60,  30,  6;
  1, 7, 42, 105, 140, 105, 42, 7;
  ...

Mathematica

Table[Max[k, 1]*Binomial[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, May 03 2024 *)

Crossrefs

Cf. A005183, A007318.

Sequence in context: A160014 A068956 A124842 * A094436 A373436 A286012

Adjacent sequences: A134396 A134397 A134398 * A134400 A134401 A134402

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 23 2007

Extensions

Corrected and edited by Olivier Gérard, Aug 01 2013

Status

approved