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 A360782 #17 Feb 21 2023 02:09:24
%S A360782 1,1,1,3,7,16,45,125,363,1127,3561,11696,39727,138113,494213,1811075,
%T A360782 6784115,25985928,101520833,404305549,1640002039,6767576175,
%U A360782 28395916893,121048681024,523902418555,2300906314849,10248029334297,46266088140291
%N A360782 Expansion of Sum_{k>=0} x^k / (1 - k*x^2)^(k+1).
%F A360782 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-k,k).
%t A360782 Join[{1}, Table[Sum[Binomial[n-k,k] * (n-2*k)^k, {k,0,n/2}], {n,1,30}]] (* _Vaclav Kotesovec_, Feb 21 2023 *)
%o A360782 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)^(k+1)))
%o A360782 (PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*binomial(n-k, k));
%Y A360782 Cf. A000248, A360783.
%Y A360782 Cf. A000045, A360592.
%K A360782 nonn,easy
%O A360782 0,4
%A A360782 _Seiichi Manyama_, Feb 20 2023