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 A383379 #11 Apr 25 2025 11:42:51
%S A383379 1,1,4,21,176,1765,22464,331177,5692672,110286441,2394828800,
%T A383379 57389046781,1507401363456,43018690418509,1326170009092096,
%U A383379 43905977120300625,1553942522589937664,58544111242378404433,2339326913228257886208,98816004834223734304741
%N A383379 a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * binomial(n+k,n)/(n-k)!.
%F A383379 a(n) = n! * [x^n] exp(-n*x) / (1-x)^(n+1).
%F A383379 a(n) ~ phi^(3*n + 3/2) * n^n / (5^(1/4) * exp(phi*n)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Apr 25 2025
%o A383379 (PARI) a(n) = n!*sum(k=0, n, (-n)^(n-k)*binomial(n+k, k)/(n-k)!);
%Y A383379 Main diagonal of A383341.
%Y A383379 Cf. A295182.
%K A383379 nonn
%O A383379 0,3
%A A383379 _Seiichi Manyama_, Apr 24 2025