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 A104872 #23 Apr 14 2022 02:27:17
%S A104872 1,0,1,1,2,3,6,12,27,64,163,441,1268,3855,12344,41464,145653,533736,
%T A104872 2036149,8071785,33192790,141351715,622384730,2829417276,13263528351,
%U A104872 64038928728,318121600695,1624347614737,8517247764136,45822087138879
%N A104872 Diagonal sums of A004248.
%H A104872 Seiichi Manyama, <a href="/A104872/b104872.txt">Table of n, a(n) for n = 0..681</a>
%F A104872 a(n) = Sum_{k=0..floor(n/2)} k^(n-2*k).
%F A104872 G.f.: Sum_{k>=0} x^(2*k) / (1 - k * x). - _Seiichi Manyama_, Apr 09 2022
%F A104872 a(n) ~ sqrt(Pi) * (n/(2*LambertW(exp(1)*n/2)))^(n + 1/2 - n/LambertW(exp(1)*n/2)) / sqrt(1 + LambertW(exp(1)*n/2)). - _Vaclav Kotesovec_, Apr 14 2022
%o A104872 (PARI) a(n) = sum(k=0, n\2, k^(n-2*k)); \\ _Seiichi Manyama_, Apr 09 2022
%o A104872 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k*x))) \\ _Seiichi Manyama_, Apr 09 2022
%Y A104872 Cf. A004248, A026898, A352944.
%K A104872 easy,nonn
%O A104872 0,5
%A A104872 _Paul Barry_, Mar 28 2005