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 A361568 #19 Jun 16 2024 11:02:15
%S A361568 1,0,0,1,12,60,130,420,8400,101080,781200,4435200,37714600,607807200,
%T A361568 8660652000,94007313400,914497584000,11566931376000,198256136478400,
%U A361568 3275456501116800,46558791351072000,636647461257808000,10238792220969312000,194852563745775936000
%N A361568 Expansion of e.g.f. exp(x^3/6 * (1+x)^3).
%F A361568 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(3*k,n-3*k)/(6^k * k!).
%F A361568 a(0) = 1; a(n) = ((n-1)!/6) * Sum_{k=3..n} k * binomial(3,k-3) * a(n-k)/(n-k)!.
%F A361568 a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 12*(n-3)*a(n-4) + 15*(n-3)*(n-4)*a(n-5) + 6*(n-3)*(n-4)*(n-5)*a(n-6)). -_Seiichi Manyama_, Jun 16 2024
%o A361568 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3/6*(1+x)^3)))
%o A361568 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/6*sum(j=3, i, j*binomial(3, j-3)*v[i-j+1]/(i-j)!)); v;
%Y A361568 Cf. A047974, A361567, A361569.
%Y A361568 Cf. A115055, A361279.
%K A361568 nonn
%O A361568 0,5
%A A361568 _Seiichi Manyama_, Mar 16 2023