A033918 Triangular array in which n-th row consists of the numbers 1^1, 2^2, ... n^n.

1, 1, 4, 1, 4, 27, 1, 4, 27, 256, 1, 4, 27, 256, 3125, 1, 4, 27, 256, 3125, 46656, 1, 4, 27, 256, 3125, 46656, 823543, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 1, 4, 27, 256, 3125, 46656

Offset: 1

Author

Timur I Khantimirov (Tim(AT)sbbank.udm.ru)

Keywords

• nonn
• tabl
• easy

Comments

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. Sequence A033918 is the reluctant sequence of A000312 (number of labeled mappings from n points to themselves, endofunctions): n^n. - Boris Putievskiy, Dec 14 2012

Examples

			1;
1, 4;
1, 4, 27;
1, 4, 27, 256;
1, 4, 27, 256, 3125;
1, 4, 27, 256, 3125, 46656;
1, 4, 27, 256, 3125, 46656, 823543;
...
		

Links

• Timur I Khantimirov and Boris Putievskiy (first 51 from Timur I Khantimirov), Table of n, a(n) for n = 1..1000
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Cf. A002260, A220415, A220416.

Programs

Mathematica

Module[{nn=10,c},c=Table[n^n,{n,nn}];Flatten[Table[Take[c,i],{i,nn}]]] (* Harvey P. Dale, Nov 02 2014 *)

Python

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

Formula

a(n) = A000312(m), where m= n-t(t+1)/2, t=floor((-1+sqrt(8*n-7))/2) or a(n)=(n-t(t+1)/2)^(n-t(t+1)/2), where t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 14 2012