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 A362080 #12 Aug 30 2025 10:33:14
%S A362080 1,1,7,55,571,7026,98925,1562219,27214867,516646333,10589130223,
%T A362080 232574622116,5440521381816,134859301929873,3527034780915985,
%U A362080 96965997588549555,2793286163779275779,84076751617833902070,2637677096916448507104
%N A362080 a(n) = [x^n] 1/(1 - x*(1+x)^n)^n.
%H A362080 Seiichi Manyama, <a href="/A362080/b362080.txt">Table of n, a(n) for n = 0..449</a>
%F A362080 a(n) = Sum_{k=0..n} (-1)^k * binomial(-n,k) * binomial(n*k,n-k) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n*k,n-k).
%o A362080 (PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n*k, n-k));
%Y A362080 Main diagonal of A362078.
%Y A362080 Main diagonal of A362079.
%Y A362080 Cf. A099237.
%K A362080 nonn,changed
%O A362080 0,3
%A A362080 _Seiichi Manyama_, Apr 08 2023