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 A380046 #10 Jan 11 2025 10:26:40
%S A380046 1,2,8,36,176,840,3312,4592,-85888,-893664,1375040,165097152,
%T A380046 2297399040,-437916544,-676590342400,-13778476089600,-35262701498368,
%U A380046 5528190100333056,159800245551129600,1036568296401259520,-77532370748157030400,-3135837171024874272768
%N A380046 E.g.f. A(x) satisfies A(x) = 1 + 2*x*exp(x)*A(x)^(1/2).
%F A380046 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380050.
%F A380046 E.g.f.: exp( 2*arcsinh(x*exp(x)) ).
%F A380046 E.g.f.: ( x*exp(x) + sqrt(1 + x^2*exp(2*x)) )^2.
%F A380046 a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(k/2+1,k)/( (k/2+1)*(n-k)! ).
%o A380046 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*asinh(x*exp(x)))))
%o A380046 (PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(k/2+1, k)/((k/2+1)*(n-k)!));
%Y A380046 Cf. A006153, A380047.
%Y A380046 Cf. A380050.
%K A380046 sign
%O A380046 0,2
%A A380046 _Seiichi Manyama_, Jan 11 2025