A220416 Table T(n,k) = ((n+k-1)*(n+k-2)/2+n)^n, n,k >0 read by antidiagonals.

1, 2, 9, 4, 25, 216, 7, 64, 729, 10000, 11, 144, 2197, 38416, 759375, 16, 289, 5832, 130321, 3200000, 85766121, 22, 529, 13824, 390625, 11881376, 387420489, 13492928512, 29, 900, 29791, 1048576, 39135393, 1544804416, 64339296875, 2821109907456

Offset: 1

Author

Boris Putievskiy, Dec 14 2012

Keywords

• nonn
• tabl

Comments

The first column is A000124.

Examples

			The start of the sequence as triangle array is:
  1;
  2,9;
  4,25,216;
  7,64,729,10000;
  11, 144, 2197, 38416, 759375;
  ...
		

Links

• Boris Putievskiy, Rows n = 1..30 of triangle, flattened
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A002260, A000124.

Programs

Python

t=int((math.sqrt(8*n-7) - 1)/ 2)
m=n**(n-t*(t+1)/2)

Formula

As a linear array, the sequence is a(n) = n^A002260(n) or

a(n) = n^(n-t(t+1)/2), where t=floor[(-1+sqrt(8*n-7))/2].