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 A351933 #22 Jun 08 2024 08:51:03
%S A351933 1,1,1,4,13,61,331,1996,14449,109873,971821,8995636,93329941,
%T A351933 1018571269,12110589583,151955795356,2037757374241,28837620752161,
%U A351933 430834395468889,6777014821152868,111663525724783741,1930478057636642221,34781068833200111731
%N A351933 Expansion of e.g.f. exp(x / (1 - x^2/2)).
%F A351933 a(n) = Sum_{k=0..floor((n-1)/2)} (2*k+1)!/2^k * binomial(n-1,2*k) * a(n-1-2*k) for n > 2.
%F A351933 a(n) ~ n^(n - 1/4) / (2^(n/2 + 5/8) * exp(n - 2^(3/4)*sqrt(n))). - _Vaclav Kotesovec_, Mar 03 2022
%F A351933 Conjecture D-finite with recurrence +4*a(n) -4*a(n-1) -4*(n-1)*(n-2)*a(n-2) -2*(n-1)*(n-2)*a(n-3) +(n-1)*(n-2)*(n-3)*(n-4)*a(n-4)=0. - _R. J. Mathar_, Mar 09 2022
%F A351933 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n-k-1,k)/(2^k * (n-2*k)!). - _Seiichi Manyama_, Jun 08 2024
%t A351933 m = 22; Range[0, m]! * CoefficientList[Series[Exp[x / (1 - x^2/2)], {x, 0, m}], x] (* _Amiram Eldar_, Feb 26 2022 *)
%o A351933 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x^2/2))))
%o A351933 (PARI) a(n) = if(n<3, 1, sum(k=0, (n-1)\2, (2*k+1)!/2^k*binomial(n-1, 2*k)*a(n-1-2*k)));
%Y A351933 Cf. A000262, A351934, A351935, A351936.
%Y A351933 Cf. A088009.
%K A351933 nonn
%O A351933 0,4
%A A351933 _Seiichi Manyama_, Feb 26 2022