OFFSET
1,2
COMMENTS
First term of n-th row is n*(n+1)/2.
Row sum are A002663 (without initial zeros).
Appears to be the triangle resulting from adding the row number (first row numbered 0) of Pascal's triangle (A007318) to each entry in that row, subtracting the corresponding entries in the triangle formed by taking the finite diagonals in the multiplication table in order of increasing length (A003991), and removing the outer two layers, which consist entirely of 0's.
LINKS
Iva Kodrnja and Helena Koncul, Number of Polynomials Vanishing on a Basis of S_m(Gamma_0(N)), arXiv:2405.10747 [math.NT], 2024. See p. 10.
EXAMPLE
Table begins
1;
3, 3;
6, 10, 6;
10, 22, 22, 10;
15, 40, 53, 40, 15;
21, 65, 105, 105, 65, 21;
28, 98, 185, 226, 185, 98, 28;
36, 140, 301, 431, 431, 301, 140, 36;
45, 192, 462, 756, 887, 756, 462, 192, 45;
...
If the zeros are included, the table begins
0;
0, 0;
0, 0, 0;
0, 0, 0, 0;
0, 0, 1, 0, 0;
0, 0, 3, 3, 0, 0;
0, 0, 6, 10, 6, 0, 0;
0, 0, 10, 22, 22, 10, 0, 0;
... - from Michael De Vlieger, May 27 2024
MATHEMATICA
a = Table[Flatten[Table[If[Binomial[m, n] - (1 +n (m - n)) == 0, {}, Binomial[m, n] - (1 + n (m - n))], {n, 0, m}]], {m, 0, 14}]
CROSSREFS
KEYWORD
nonn,tabf,uned
AUTHOR
Roger L. Bagula, Jun 26 2007
STATUS
approved