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 A354519 #25 Apr 15 2023 15:25:11
%S A354519 0,1,3,8,20,61,203,888,4080,24001,140283,1028048,7248020,63374221,
%T A354519 522164243,5299033488,49924707840,576514338721,6110861416083,
%U A354519 79100066353208,931434877343540,13355627237749501,172948115797623803,2720827878727067208,38424408320191299120
%N A354519 Expansion of e.g.f. exp(x) * log(sec(x)).
%F A354519 a(n) = Sum_{k=1..floor(n/2)} A000182(k) * binomial(n,2*k).
%F A354519 a(n) ~ 2^(n + 1/2) * (exp(Pi/2) + (-1)^n/exp(Pi/2)) * n^(n - 1/2) / (Pi^(n - 1/2) * exp(n)). - _Vaclav Kotesovec_, Aug 17 2022
%o A354519 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(exp(x)*log(1/cos(x)))))
%o A354519 (PARI) a(n) = sum(k=1, n\2, ((-4)^k-(-16)^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));
%o A354519 (Python)
%o A354519 from math import comb
%o A354519 from sympy import bernoulli
%o A354519 def A354519(n): return sum(abs(((2-(2<<(m:=k<<1)))*bernoulli(m)<<m-2)//k)*comb(n,k<<1) for k in range(1,(n>>1)+1)) # _Chai Wah Wu_, Apr 15 2023
%Y A354519 Cf. A000182, A354517, A354520.
%K A354519 nonn
%O A354519 1,3
%A A354519 _Seiichi Manyama_, Aug 16 2022