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 A368173 #15 Jan 22 2025 06:38:45
%S A368173 0,0,0,3,6,10,105,651,2968,26496,265905,2203795,22830456,288661308,
%T A368173 3476579197,44960585775,671394654960,10329701480416,164573071219233,
%U A368173 2865785889662019,52647629639499280,1000194250108913580,20125846165307543661,426789766980101676943
%N A368173 Expansion of e.g.f. -log(1 - x^2/2 * (exp(x) - 1)).
%H A368173 Seiichi Manyama, <a href="/A368173/b368173.txt">Table of n, a(n) for n = 0..454</a>
%F A368173 a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * Stirling2(n-2*k,k)/(2^k * (n-2*k)!).
%F A368173 a(0) = a(1) = a(2) = 0; a(n) = n*(n-1)/2 + Sum_{k=3..n-1} k*(k-1)/2 * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Jan 22 2025
%o A368173 (PARI) a(n) = n!*sum(k=1, n\3, (k-1)!*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));
%Y A368173 Cf. A052858, A368174.
%Y A368173 Cf. A353998.
%K A368173 nonn
%O A368173 0,4
%A A368173 _Seiichi Manyama_, Dec 14 2023