A320251 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of 1/(1 - Sum_{j>=1} j^k*x^j).
1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 5, 8, 8, 1, 1, 9, 18, 21, 16, 1, 1, 17, 44, 63, 55, 32, 1, 1, 33, 114, 207, 221, 144, 64, 1, 1, 65, 308, 723, 991, 776, 377, 128, 1, 1, 129, 858, 2631, 4805, 4752, 2725, 987, 256, 1, 1, 257, 2444, 9843, 24655, 31880, 22769, 9569, 2584, 512
Offset: 0
Examples
G.f. of column k: A_k(x) = 1 + x + (2^k + 1)*x^2 + (2^(k + 1) + 3^k + 1)*x^3 + (3*2^k + 2^(2*k + 1) + 2*3^k + 1)*x^4 + ... Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, ... 2, 3, 5, 9, 17, 33, ... 4, 8, 18, 44, 114, 308, ... 8, 21, 63, 207, 723, 2631, ... 16, 55, 221, 991, 4805, 24655, ...
Links
- N. J. A. Sloane, Transforms
Crossrefs
Programs
-
Mathematica
Table[Function[k, SeriesCoefficient[1/(1 - Sum[i^k x^i, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten Table[Function[k, SeriesCoefficient[1/(1 - PolyLog[-k, x]), {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
Formula
G.f. of column k: 1/(1 - PolyLog(-k,x)), where PolyLog() is the polylogarithm function.
Comments