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 A383121 #10 Apr 17 2025 14:54:44
%S A383121 1,0,3,47,1093,33029,1236781,55325416,2879987209,171061709417,
%T A383121 11418368571721,846230146390001,68949300160035373,6126085419697733567,
%U A383121 589470974371501065845,61068847238080533844679,6777270943578364524130321,802138434294752321142680145
%N A383121 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k).
%F A383121 a(n) = [x^n] ((1 + x)^n - x)^n.
%F A383121 a(n) ~ exp(n - exp(-1) - 1/2) * n^n / sqrt(2*Pi*n). - _Vaclav Kotesovec_, Apr 17 2025
%t A383121 Table[Sum[(-1)^(n - k) Binomial[n, k] Binomial[n k, k], {k, 0, n}], {n, 0, 17}]
%o A383121 (PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(n,k) * binomial(n*k,k)); \\ _Michel Marcus_, Apr 17 2025
%Y A383121 Cf. A002426, A349471, A378409, A383118, A383119, A383120.
%K A383121 nonn
%O A383121 0,3
%A A383121 _Ilya Gutkovskiy_, Apr 17 2025