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 A373758 #10 Jun 17 2024 08:50:28
%S A373758 1,0,0,0,1,10,90,840,8435,91980,1089900,13998600,194184375,2897744850,
%T A373758 46335539250,790936146000,14361717995625,276491756541000,
%U A373758 5626652076045000,120696581303298000,2722068344529158625,64392333741216731250,1594243471325576321250
%N A373758 Expansion of e.g.f. exp(x^4/(24 * (1 - x)^2)).
%F A373758 a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-2*k-1,n-4*k)/(24^k * k!).
%F A373758 a(0) = 1; a(n) = ((n-1)!/24) * Sum_{k=4..n} k * (k-3) * a(n-k)/(n-k)!.
%o A373758 (PARI) a(n) = n!*sum(k=0, n\4, binomial(n-2*k-1, n-4*k)/(24^k*k!));
%o A373758 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/24*sum(j=4, i, j*(j-3)*v[i-j+1]/(i-j)!)); v;
%Y A373758 Cf. A361545, A361577, A373759.
%K A373758 nonn
%O A373758 0,6
%A A373758 _Seiichi Manyama_, Jun 17 2024