A219356 Triangle read by rows: A219274 with rows reversed.

1, 1, 1, 1, 2, 1, 3, 1, 4, 5, 1, 5, 9, 16, 1, 6, 14, 49, 1, 7, 20, 92, 70, 1, 8, 27, 153, 204, 168, 1, 9, 35, 235, 405, 738, 768, 1, 10, 44, 341, 715, 1815, 3300, 1, 11, 54, 474, 1166, 3630, 9460, 7887, 1, 12, 65, 637, 1794, 6578, 21307, 28743, 15015

Offset: 0

Author

Alois P. Heinz, Nov 18 2012

Keywords

• nonn
• tabf

Comments

For more information see A219274.

Examples

			A219274 with rows reversed begins:
  1;
  1;
  1;
  1,  2;
  1,  3;
  1,  4,  5;
  1,  5,  9,  16;
  1,  6, 14,  49;
  1,  7, 20,  92,  70;
  1,  8, 27, 153, 204, 168;
  1,  9, 35, 235, 405, 738, 768;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..100, flattened

Crossrefs

Row lengths are A122797 (for n>0).

Row sums give: A218293.

Last elements of rows give: A219339.

Programs

Maple

h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
      add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
    end:
g:= proc(n, i, l) local s; s:=i*(i+1)/2;
      `if`(n=s, h([l[], seq(i-j, j=0..i-1)]), `if`(n>s, 0,
       g(n, i-1, l)+ `if`(i>n, 0, g(n-i, i-1, [l[], i]))))
    end:
T:= (n, k)-> `if`(k>n, 0, g(n-k, k-1, [k])):
seq(seq(T(n, n-k), k=0..(n-floor(sqrt(2*n)+1/2))), n=0..14);