A092393 Triangle read by rows: T(n,k) = (n+k)*binomial(n,k) (for k=0..n-1).

1, 2, 6, 3, 12, 15, 4, 20, 36, 28, 5, 30, 70, 80, 45, 6, 42, 120, 180, 150, 66, 7, 56, 189, 350, 385, 252, 91, 8, 72, 280, 616, 840, 728, 392, 120, 9, 90, 396, 1008, 1638, 1764, 1260, 576, 153, 10, 110, 540, 1560, 2940, 3780, 3360, 2040, 810, 190, 11, 132, 715

Offset: 1

Author

Benoit Cloitre, Mar 21 2004

Keywords

• nonn
• tabl

Examples

			Triangle starts:
1;
2, 6;
3, 12, 15;
4, 20, 36,  28;
5, 30, 70,  80,  45;
6, 42, 120, 180, 150, 66;
...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..11325 (rows 1..150 of the triangle, flattened)

Crossrefs

Cf. A029635.

Programs

Maple

A092393 := proc(n,k)
    (n+k)*binomial(n,k) ;
end proc:
seq(seq( A092393(n,k),k=0..n-1),n=1..12) ; # R. J. Mathar, Nov 02 2023

Mathematica

A092393row[n_]:=Table[(n+k)Binomial[n,k],{k,0,n-1}];Array[A092393row,10]  (* Paolo Xausa, Nov 02 2023 *)

PARI

T(n,k)=binomial(n,k)*(n+k)

Formula

First column = positive integers;

second column = A002378;

third column = A077414;

main diagonal (i.e., T(n,n) = (n+n)*binomial(n,n) = 2n, which is not included in this sequence) = even integers;

second diagonal = A000384.

Row sums = 1, 8, 30, 88, 230,... = A167667(n)-2n. - R. J. Mathar, Nov 02 2023