OFFSET
0,9
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
G.f. of column k: Product_{j>=1} (1+x^j)^(j^k).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, 64, 128, ...
2, 5, 13, 35, 97, 275, 793, 2315, ...
2, 8, 31, 119, 457, 1763, 6841, 26699, ...
3, 16, 83, 433, 2297, 12421, 68393, 382573, ...
4, 28, 201, 1476, 11113, 85808, 678101, 5466916, ...
5, 49, 487, 4962, 52049, 561074, 6189117, 69540142, ...
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*binomial(i^k, j), j=0..n/i)))
end:
A:= (n, k)-> b(n$2, k):
seq(seq(A(n, d-n), n=0..d), d=0..14); # Alois P. Heinz, Oct 16 2017
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
Sum[b[n - i*j, i - 1, k]*Binomial[i^k, j], {j, 0, n/i}]]];
A[n_, k_] := b[n, n, k];
Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-François Alcover, Feb 10 2021, after Alois P. Heinz *)
CROSSREFS
Main diagonal gives A270917.
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 07 2017
STATUS
approved