OFFSET
0,82
COMMENTS
Equals A181506 when the first column is removed. - Georg Fischer, Jul 26 2023
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
FORMULA
T(n,k) = [x^n y^k] 1/Product_{j>=1} (1-y*x^A000217(j)).
EXAMPLE
Triangle T(n,k) begins:
1;
0, 1;
0, 0, 1;
0, 1, 0, 1;
0, 0, 1, 0, 1;
0, 0, 0, 1, 0, 1;
0, 1, 1, 0, 1, 0, 1;
0, 0, 1, 1, 0, 1, 0, 1;
0, 0, 0, 1, 1, 0, 1, 0, 1;
0, 0, 1, 1, 1, 1, 0, 1, 0, 1;
0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1;
0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1;
0, 0, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1;
MAPLE
h:= proc(n) option remember; `if`(n<1, 0,
`if`(issqr(8*n+1), n, h(n-1)))
end:
b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
b(n, h(i-1))+expand(x*b(n-i, h(min(n-i, i)))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n, h(n))):
seq(T(n), n=0..20);
MATHEMATICA
h[n_] := h[n] = If[n < 1, 0, If[IntegerQ @ Sqrt[8*n + 1], n, h[n - 1]]];
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, x^n, b[n, h[i - 1]] + Expand[ x*b[n - i, h[Min[n - i, i]]]]];
T[n_] := Table[Coefficient[#, x, i], {i, 0, n}]& @ b[n, h[n]];
Table[T[n], {n, 0, 20}] // Flatten (* Jean-François Alcover, May 27 2019, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 28 2018
STATUS
approved