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%I #33 Nov 19 2021 17:48:04
%S 0,1,1,5,9,44,114,564,1882,9665,39083,211025,993803,5686104,30342060,
%T 184813048,1095555260,7118824417,46199135453,320295658577,
%U 2250749112381,16626717667348,125452246988974,985178854556524
%N Sum of all the smaller parts raised to their corresponding larger parts of the partitions of n into exactly two parts.
%H G. C. Greubel, <a href="/A226065/b226065.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i = 1..floor(n/2)} i^(n-i).
%e a(6) = 44; 6 has exactly 3 partitions into two parts: (5,1),(4,2),(3,3). Raising the smaller parts to their corresponding larger parts and adding the results, we get: 1^5 + 2^4 + 3^3 = 1 + 16 + 27 = 44.
%t Table[Sum[i^(n - i), {i, Floor[n/2]}], {n,50}] (* _G. C. Greubel_, Dec 13 2016 *)
%o (PARI) a(n)=sum(i=1,floor(n/2),i^(n-i)) \\ _Ralf Stephan_, May 27 2013
%Y Cf. A226140.
%K nonn,easy
%O 1,4
%A _Wesley Ivan Hurt_, May 24 2013
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