A127952 Triangle read by rows, T(n,k) = (n+1)*binomial(n-1,k-1).

1, 0, 2, 0, 3, 3, 0, 4, 8, 4, 0, 5, 15, 15, 5, 0, 6, 24, 36, 24, 6, 0, 7, 35, 70, 70, 35, 7, 0, 8, 48, 120, 160, 120, 48, 8, 0, 9, 63, 189, 315, 315, 189, 63, 9, 0, 10, 80, 280, 560, 700, 560, 280, 80, 10, 0, 11, 99, 396, 924, 1386, 1386, 924, 396, 99, 11

Offset: 0

Author

Gary W. Adamson, Feb 09 2007

Keywords

• nonn
• tabl

Comments

Row sums = A057711, starting (1, 2, 6, 16, 40, 96, ...).

T(2n,n) gives A033876(n-1) for n > 0. - Alois P. Heinz, Sep 04 2014

Examples

			First few rows of the triangle:
  1;
  0, 2;
  0, 3,  3;
  0, 4,  8,  4;
  0, 5, 15, 15,  5;
  0, 6, 24, 36, 24,  6;
  0, 7, 35, 70, 70, 35,  7;
  ...
		

Links

• G. C. Greubel, Rows n=0..100 of triangle, flattened

Crossrefs

Cf. A007318, A126615, A057711.

Programs

Magma

[[n le 0 select 1 else (n+1)*Binomial(n-1,k-1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 05 2018

Maple

T := (n,k) -> (n+1)*binomial(n-1, k-1);
seq(print(seq(T(n,k),k= 0..n)),n=0..6); # Peter Luschny, Sep 02 2014

Mathematica

Table[(n+1)*Binomial[n-1, k-1], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, May 05 2018 *)

PARI

for(n=0,10, for(k=0,n, print1(if(n==0, 1,(n+1)*binomial(n-1,k-1)), ", "))) \\ G. C. Greubel, May 05 2018

Extensions

Name corrected after a suggestion of Joerg Arndt by Peter Luschny, Sep 02 2014