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, 823543, 16777216, 387420489, 10000000000

Offset

1,3

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

Links

Boris Putievskiy, Table of n, a(n) for n = 1..1000

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

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

Example

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;
...

Mathematica

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

Prog

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

Crossrefs

Cf. A002260, A220415, A220416.

Sequence in context: A143461 A066808 A363935 * A136467 A079188 A076810

Adjacent sequences: A033915 A033916 A033917 * A033919 A033920 A033921

Keyword

nonn,tabl,easy

Author

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

Status

approved