A134836 Antidiagonals of the array: A007318 * A002260(transposed).

1, 1, 1, 1, 3, 1, 1, 5, 3, 1, 1, 7, 8, 3, 1, 1, 9, 16, 8, 3, 1, 1, 11, 27, 20, 8, 3, 1, 1, 13, 41, 43, 20, 8, 3, 1, 1, 15, 58, 81, 48, 20, 8, 3, 1, 1, 17, 78, 138, 106, 48, 20, 8, 3, 1, 1, 19, 101, 218, 213, 112, 48, 20, 8, 3, 1

Offset: 1

Author

Gary W. Adamson, Nov 12 2007

Keywords

• nonn
• tabl
• easy

Comments

Antidiagonals tend to A001792 starting from the right: (1, 3, 8, 20, 48, 112, ...).

Examples

			First few rows of the array:
  1,  1,  1,  1,   1,   1, ...;
  1,  3,  3,  3,   3,   3, ...;
  1,  5,  8,  8,   8,   8, ...;
  1,  7, 16, 20,  20,  20, ...;
  1,  9, 27, 43,  48,  48, ...;
  1, 11, 41, 81, 106, 112, ...;
  ...
First few rows of the triangle:
  1;
  1,  1;
  1,  3,  1;
  1,  5,  3,  1;
  1,  7,  8,  3,  1;
  1,  9, 16,  8,  3,  1;
  1, 11, 27, 20,  8,  3,  1;
  1, 13, 41, 43, 20,  8,  3,  1;
  ...
		

Crossrefs

Cf. A002260, A001792, A116445 (array transposed), A001629 (antidiagonal sums).

Programs

Maple

A002260 := proc(n,k)
    if n <= k then
        n+1;
    else
        0 ;
    end if;
end proc:
A007318 := proc(n,k)
    if k <= n then
        binomial(n,k) ;
    else
        0
    end if;
end proc:
A134836 := proc(n,k)
    add( A007318(n,i)*A002260(i,k),i=0..k) ;
end proc:
seq(seq(A134836(d-k,k),k=0..d),d=0..12) ; # R. J. Mathar, Aug 17 2022

Formula

Antidiagonals of the array: A007318 * A002260(transform), where A002260 = (1; 1,2; 1,2,3; ...).

Extensions

One term corrected by R. J. Mathar, Aug 17 2022