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

1,2

Comments

The first column is A000124.

Links

Boris Putievskiy, Rows n = 1..30 of triangle, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

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].

Example

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

Prog

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

Crossrefs

Cf. A002260, A000124.

Sequence in context: A318680 A171560 A302451 * A054789 A002508 A353242

Adjacent sequences: A220413 A220414 A220415 * A220417 A220418 A220419

Keyword

nonn,tabl

Author

Boris Putievskiy, Dec 14 2012

Status

approved