OFFSET
0,9
LINKS
Alois P. Heinz, Rows n = 0..150, flattened
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, ...
2, 5, 13, 35, 97, ...
2, 7, 25, 91, 337, ...
MAPLE
b:= proc(n, i, k) option remember; (m->
`if`(m<n, 0, `if`(n=m, i!^k, b(n, i-1, k)+
`if`(i>n, 0, i^k*b(n-i, i-1, k)))))(i*(i+1)/2)
end:
A:= (n, k)-> b(n$2, k):
seq(seq(A(n, d-n), n=0..d), d=0..14); # Alois P. Heinz, Sep 11 2017
MATHEMATICA
m = 14;
col[k_] := col[k] = Product[1 + j^k*x^j, {j, 1, m}] + O[x]^(m+1) // CoefficientList[#, x]&;
A[n_, k_] := col[k][[n+1]];
Table[A[n, d-n], {d, 0, m}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 11 2021 *)
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Sep 11 2017
STATUS
approved