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 A373770 #10 Jun 18 2024 10:01:25
%S A373770 1,1,3,12,63,405,3075,26880,265545,2922885,35447895,469396620,
%T A373770 6736095135,104102463465,1723322736135,30416726340000,570089983287825,
%U A373770 11306156398562025,236514323713142475,5204122351983254700,120139520273298100575,2903216115946088267325
%N A373770 Expansion of e.g.f. exp(x^2 / (2 * (1 - x))) / (1 - x).
%F A373770 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n-k,n-2*k)/(2^k * k!).
%F A373770 From _Vaclav Kotesovec_, Jun 18 2024: (Start)
%F A373770 Recurrence: 2*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-2)*(n-1)*a(n-2) - (n-2)*(n-1)*a(n-3).
%F A373770 a(n) ~ 2^(-1/4) * exp(-3/4 + sqrt(2*n) - n) * n^(n + 1/4) * (1 + 7/(6*sqrt(2*n))). (End)
%o A373770 (PARI) a(n) = n!*sum(k=0, n\2, binomial(n-k, n-2*k)/(2^k*k!));
%Y A373770 Cf. A130905, A361596, A373771.
%Y A373770 Cf. A185369.
%K A373770 nonn
%O A373770 0,3
%A A373770 _Seiichi Manyama_, Jun 18 2024