login
A290054
Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Sum_{j>=0} x^(j^3))^k.
8
1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 6, 1, 0, 0, 0, 1, 6, 10, 4, 0, 0, 0, 0, 1, 7, 15, 10, 1, 0, 0, 0, 0, 1, 8, 21, 20, 5, 0, 0, 0, 1, 0, 1, 9, 28, 35, 15, 1, 0, 0, 2, 0, 0, 1, 10, 36, 56, 35, 6, 0, 0, 3, 2, 0, 0, 1, 11, 45, 84, 70, 21, 1, 0, 4, 6, 0, 0, 0
OFFSET
0,8
COMMENTS
A(n,k) is the number of ways of writing n as a sum of k nonnegative cubes.
FORMULA
G.f. of column k: (Sum_{j>=0} x^(j^3))^k.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 0, 1, 3, 6, 10, ...
0, 0, 0, 1, 4, 10, ...
0, 0, 0, 0, 1, 5, ...
0, 0, 0, 0, 0, 1, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Sum[x^i^3, {i, 0, n}]^k, {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
CROSSREFS
Main diagonal gives A291700.
Antidiagonal sums give A302019.
Sequence in context: A325466 A077029 A052553 * A290430 A290429 A045847
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Jul 19 2017
STATUS
approved