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a(0) = 1; for n>0: a(n) = sum{a(i)*n^i : 0<=i<n}.
1

%I #27 Jan 10 2015 09:18:20

%S 1,1,3,31,2037,1277081,9933228619,1168655882598723,

%T 2450851625481815985865,105501131724162360454576400809,

%U 105501131969247534689326758739077501311,2736427656021274732181782085698646439681516475371

%N a(0) = 1; for n>0: a(n) = sum{a(i)*n^i : 0<=i<n}.

%H Reinhard Zumkeller, <a href="/A066976/b066976.txt">Table of n, a(n) for n = 0..32</a>

%e a(3) = a(0)*3^0 + a(1)*3^1 + a(2)*3^2 = 1*1 + 1*3 + 3*9 = 31.

%p a:= proc(n) option remember;

%p `if`(n=0, 1, add(a(i)*n^i, i=0..n-1))

%p end:

%p seq(a(n), n=0..15); # _Alois P. Heinz_, Aug 21 2011

%t a[0] = 1; a[n_] := Sum[a[i]*n^i, {i, 0, n-1}]; Table[a[n], {n, 0, 11}] (* _Jean-François Alcover_, Mar 24 2014 *)

%o (Haskell)

%o a066976 0 = 1

%o a066976 n = sum $ zipWith (*) a066976_list $ map (n ^) [0..n-1]

%o a066976_list = map a066976 [0..]

%o -- _Reinhard Zumkeller_, Oct 25 2011

%K nonn,nice

%O 0,3

%A _Reinhard Zumkeller_, Jan 26 2002