This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226140 #32 Mar 25 2025 12:05:22
%S A226140 0,1,2,7,13,48,95,424,898,4837,10780,68399,158111,1156224,2745145,
%T A226140 22744380,55098660,510307001,1255610350,12859037607,32030878113,
%U A226140 359498491968,904385401323,11040700820704,28000658588542
%N A226140 a(n) = Sum_{i=1..floor(n/2)} (n-i)^i.
%C A226140 a(n) is the sum of the larger parts raised to the corresponding smaller parts of the partitions of n into exactly two parts.
%H A226140 Michael De Vlieger, <a href="/A226140/b226140.txt">Table of n, a(n) for n = 1..773</a>
%H A226140 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A226140 a(n) = Sum_{i=1..floor(n/2)} (n-i)^i.
%e A226140 a(6) = 48; 6 has exactly 3 partitions into two parts: (5,1),(4,2),(3,3). Raising the larger parts to their corresponding smaller parts and adding the results, we get: 5^1 + 4^2 + 3^3 = 5 + 16 + 27 = 48.
%p A226140 A226140:=n->sum((n-i)^i, i=1..n/2): seq(A226140(n), n=1..40);
%t A226140 Array[Sum[(# - i)^i, {i, Floor[#/2]}] &, 25] (* _Michael De Vlieger_, Jan 23 2018 *)
%t A226140 Table[Total[#[[1]]^#[[2]]&/@IntegerPartitions[n,{2}]],{n,30}] (* _Harvey P. Dale_, Mar 25 2025 *)
%o A226140 (PARI) a(n) = sum(k=1, n\2, (n-k)^k); \\ _Michel Marcus_, Dec 13 2015
%Y A226140 Cf. A226065.
%K A226140 nonn,easy
%O A226140 1,3
%A A226140 _Wesley Ivan Hurt_, May 27 2013