|
%I #23 Feb 15 2022 12:56:27
%S 1,1,4,1,4,27,1,4,27,256,1,4,27,256,3125,1,4,27,256,3125,46656,1,4,27,
%T 256,3125,46656,823543,1,4,27,256,3125,46656,823543,16777216,1,4,27,
%U 256,3125,46656,823543,16777216,387420489,1,4,27,256,3125,46656
%N Triangular array in which n-th row consists of the numbers 1^1, 2^2, ... n^n.
%C 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
%H Timur I Khantimirov and Boris Putievskiy (first 51 from Timur I Khantimirov), <a href="/A033918/b033918.txt">Table of n, a(n) for n = 1..1000</a>
%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F 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
%e 1;
%e 1, 4;
%e 1, 4, 27;
%e 1, 4, 27, 256;
%e 1, 4, 27, 256, 3125;
%e 1, 4, 27, 256, 3125, 46656;
%e 1, 4, 27, 256, 3125, 46656, 823543;
%e ...
%t Module[{nn=10,c},c=Table[n^n,{n,nn}];Flatten[Table[Take[c,i],{i,nn}]]] (* _Harvey P. Dale_, Nov 02 2014 *)
%o (Python)
%o t=int((math.sqrt(8*n-7) - 1)/ 2)
%o m=(n-t*(t+1)/2)**(n-t*(t+1)/2)
%Y Cf. A002260, A220415, A220416.
%K nonn,tabl,easy
%O 1,3
%A Timur I Khantimirov (Tim(AT)sbbank.udm.ru)
|
