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a(1) = 1; for n > 1, a(n) = Sum{a(n-k)^k | 0<k<n}.
1

%I #12 Oct 19 2017 03:14:06

%S 1,1,2,4,10,36,218,2804,108074,20114564,36066331898,1729247065742228,

%T 9575643422153401723466,50068381739089423185661226445092,

%U 5264344550636729304011557445558608029761914394

%N a(1) = 1; for n > 1, a(n) = Sum{a(n-k)^k | 0<k<n}.

%H Reinhard Zumkeller, <a href="/A076132/b076132.txt">Table of n, a(n) for n = 1..20</a>

%e a(2) = a(1)^1 = 1^1 = 1.

%e a(3) = a(2)^1 + a(1)^2 = 1^1 + 1^2 = 2.

%e a(4) = a(3)^1 + a(2)^2 + a(1)^3 = 2^1 + 1^2 + 1^3 = 4.

%e a(5) = a(4)^1 + a(3)^2 + a(2)^3 + a(1)^4 = 4^1 + 2^2 + 1^3 + 1^4 = 10.

%o (Haskell)

%o a076132 n = a076132_list !! (n-1)

%o a076132_list = 1 : f [1] where

%o f xs = y : f (y : xs) where y = sum $ zipWith (^) xs [1..]

%o -- _Reinhard Zumkeller_, Mar 10 2013

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Oct 30 2002

%E Corrected by _Don Reble_, Nov 20 2006