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 A249489 #11 Oct 15 2018 16:25:43
%S A249489 1,0,9,0,12070,0,126447741,0,5100496997940,0,562605048135059545,0,
%T A249489 138523311740417986721274,0,66543520389763227261554370645,0,
%U A249489 56664734898911130799849838608991176,0,79610326854782816434044397510470501877041
%N A249489 a(n) = [x^n/n!] Sum_{k=0..n} cosh(k*x)^k.
%H A249489 Vaclav Kotesovec, <a href="/A249489/b249489.txt">Table of n, a(n) for n = 0..220</a>
%F A249489 a(n) = Sum_{k=0..n} Sum_{j=0..k} binomial(k, j) * k^n * (k-2*j)^n / 2^k. [Explicitly stating Vaclav's formula in Mma program - _Paul D. Hanna_, Oct 15 2018]
%F A249489 If n is even, then a(n) ~ c * (1-2*r)^n * n^(2*n) / (2^n * exp(n) * (r*(1-r))^(n/2)), where r = 0.0832217201995176507819192648878903254298041... is the root of the equation (r/(1-r))^(1-2*r) = exp(-2), and c = 2.09233700490262732901066903251002074102409436600891921766318742438...
%t A249489 Flatten[{1,Table[Sum[Sum[Binomial[k,j] * k^n*(k-2*j)^n / 2^k,{j,0,k}],{k,0,n}],{n,1,20}]}]
%o A249489 (PARI) {a(n)=n!*polcoeff(sum(k=0, n, cosh(k*x+x*O(x^n))^k), n)}
%o A249489 for(n=0, 20, print1(a(n), ", "))
%o A249489 (PARI) {a(n) = sum(k=0,n,sum(j=0,k, binomial(k, j) * k^n*(k-2*j)^n / 2^k ))}
%o A249489 for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Oct 15 2018, using Vaclav's formula.
%Y A249489 Cf. A224899, A249459, A245322, A221077, A221078.
%K A249489 nonn
%O A249489 0,3
%A A249489 _Vaclav Kotesovec_, Oct 30 2014
%E A249489 Name clarified by _Paul D. Hanna_, Oct 15 2018