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%I #24 Jan 28 2023 08:35:38
%S 1,3,14,100,979,12201,184820,3297456,67731333,1574304985,40851766526,
%T 1170684360924,36720042483591,1251308658130545,46034015337733480,
%U 1818399978159990976,76762718946972480009
%N Sum of the (n-1)-th powers of the first n integers.
%C a(n) is the number of length n sequences of [n] who start by their maximum value.
%C By symmetry, counts a lot of other simple classes of endofunctions.
%H Seiichi Manyama, <a href="/A076015/b076015.txt">Table of n, a(n) for n = 1..387</a>
%F a(n) = Sum_{m=1..n} m^(n-1), n>=1.
%e The 3 sequences for n=2 are
%e 11, 21,22
%e The 14 = 3^0 + 3^1 + 3^2 sequences starting by their max value for n=3 are
%e 111, 211,212,221,222, 311,312,313,321,322,323,331,332,333
%p a:=n->sum((n-j+1)^n,j=0..n): seq(a(n), n=0..17); # _Zerinvary Lajos_, Jun 05 2008
%t f[n_]:=Module[{s=0},Do[s+=a^n,{a,0,n+1}]; s]; Table[f[n],{n,20}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2010 *)
%t Table[Sum[m^(n-1),{m,n}],{n,20}] (* _Harvey P. Dale_, Jan 26 2016 *)
%o (PARI) vector(20, n, sum(m=1, n, m^(n-1))) \\ _Michel Marcus_, Jan 14 2015
%Y Cf. A076014.
%Y A diagonal of array A103438.
%Y A subset of A000312.
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Oct 02 2002
%E Definition changed and example added by _Olivier Gérard_, Jan 28 2023
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