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
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.
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
KEYWORD
AUTHOR
Timur I Khantimirov (Tim(AT)sbbank.udm.ru)
STATUS
approved