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

0,13

Links

Alois P. Heinz, Antidiagonals n = 0..140, flattened

Formula

A(n,k) = A258851(n^k) = k * n^(k-1) * A258851(n).

Example

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, ...

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);

Crossrefs

Rows n=0+1,2,3,4,8 give: A000004, A001787, A212697, A018215, A230539.

Columns k=0,1 give: A000004, A258851.

Main diagonal gives A258846.

Cf. A000720.

Sequence in context: A028572 A107492 A159257 * A232833 A256269 A256279

Adjacent sequences: A258994 A258995 A258996 * A258998 A258999 A259000

Keyword

nonn,tabl

Author

Alois P. Heinz, Jun 27 2015

Status

approved