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 A345632 #16 Jun 21 2021 10:48:49
%S A345632 1,1,5,28,353,3376,66637,908608,24405761,432891136,14712104501,
%T A345632 321504185344,13218256749601,343360783937536,16565151205544957,
%U A345632 498676704524517376,27614800115689879553,945381827279671853056,59095217374989483261925,2267322327322331161821184,157904201452248753415276001
%N A345632 Sum of terms of even index in the binomial decomposition of n^(n-1).
%C A345632 When writing n^(n-1) (A000169) as a sum of powers of n using the binomial theorem, one can separately sum the even and the odd powers of n. This is the even part.
%F A345632 a(n+1) = Sum_{k=0..floor(n/2)} n^(2k) binomial(n, 2k).
%F A345632 a(n+1) = ((1 - n)^n + (1 + n)^n)/2. - _Stefano Spezia_, Jun 21 2021
%t A345632 Table[Plus @@ Table[(n-1)^(2 k) Binomial[n-1, 2 k], {k, 0, Floor[n/2]}], {n, 1, 21}]
%Y A345632 Cf. A345633 (odd part).
%Y A345632 Cf. A062024, A302583.
%Y A345632 Cf. A000169, A007778, A092364, A081131.
%K A345632 nonn,easy
%O A345632 1,3
%A A345632 _Olivier Gérard_, Jun 21 2021