A258997 A(n,k) = pi-based antiderivative of n^k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 2, 0, 0, 0, 12, 12, 4, 0, 0, 0, 32, 54, 32, 3, 0, 0, 0, 80, 216, 192, 30, 7, 0, 0, 0, 192, 810, 1024, 225, 84, 4, 0, 0, 0, 448, 2916, 5120, 1500, 756, 56, 12, 0, 0, 0, 1024, 10206, 24576, 9375, 6048, 588, 192, 12, 0
Offset: 0
Examples
Square array A(n,k) begins: 0, 0, 0, 0, 0, 0, 0, 0, ... 0, 0, 0, 0, 0, 0, 0, 0, ... 0, 1, 4, 12, 32, 80, 192, 448, ... 0, 2, 12, 54, 216, 810, 2916, 10206, ... 0, 4, 32, 192, 1024, 5120, 24576, 114688, ... 0, 3, 30, 225, 1500, 9375, 56250, 328125, ... 0, 7, 84, 756, 6048, 45360, 326592, 2286144, ... 0, 4, 56, 588, 5488, 48020, 403368, 3294172, ...
Links
- Alois P. Heinz, Antidiagonals n = 0..140, flattened
Crossrefs
Programs
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Maple
with(numtheory): d:= n-> n*add(i[2]*pi(i[1])/i[1], i=ifactors(n)[2]): A:= (n, k)-> `if`(k=0, 0, k*n^(k-1)*d(n)): seq(seq(A(n, h-n), n=0..h), h=0..14);
Comments