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 A295611 #13 Feb 16 2025 08:33:52
%S A295611 1,0,0,6,-30,-280,35070,-2508268,-47103462,241470400824,
%T A295611 -256752145545390,128291714550379292,2203924344437376054780,
%U A295611 -37693423679943326954848176,485163732930867224220253809178,27101025121379607823580070619517816
%N A295611 a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)^k.
%H A295611 Seiichi Manyama, <a href="/A295611/b295611.txt">Table of n, a(n) for n = 0..75</a>
%H A295611 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>
%F A295611 a(n) = Sum_{k=0..n} (-1)^k*A219206(n,k).
%F A295611 Limit n->infinity |a(n)|^(1/n^2) = r^(r^2/(1-2*r)) = 1.533628065110458582053143..., where r = A220359 = 0.70350607643066243096929661621777... is the real root of the equation (1-r)^(2*r-1) = r^(2*r). - _Vaclav Kotesovec_, Nov 25 2017
%t A295611 Table[Sum[(-1)^k Binomial[n, k]^k, {k, 0, n}], {n, 0, 15}]
%t A295611 Table[Sum[(-1)^k (n!/(k! (n - k)!))^k, {k, 0, n}], {n, 0, 15}]
%o A295611 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n,k)^k); \\ _Michel Marcus_, Nov 25 2017
%Y A295611 Cf. A167008, A167010, A219206.
%K A295611 sign
%O A295611 0,4
%A A295611 _Ilya Gutkovskiy_, Nov 24 2017