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 A385369 #22 Jun 29 2025 09:33:45
%S A385369 1,1,1,0,-3,0,45,0,-1575,0,99225,0,-9823275,0,1404728325,0,
%T A385369 -273922023375,0,69850115960625,0,-22561587455281875,0,
%U A385369 9002073394657468125,0,-4348001449619557104375,0,2500100833531245335015625,0,-1687568062633590601135546875,0
%N A385369 Expansion of e.g.f. x + sqrt(x^2 + 1).
%F A385369 E.g.f.: exp(arcsinh(x)).
%F A385369 E.g.f. A(x) satisfies A(x) = 1/A(-x).
%F A385369 a(n) = Sum_{k=0..n} i^(n-k) * A385343(n,k), where i is the imaginary unit.
%F A385369 a(n) = A177698(n-1) for n > 1.
%F A385369 a(2*n+1) = 0 for n > 0.
%F A385369 a(n) = 2^n * n! * binomial((n+1)/2,n)/(n+1).
%o A385369 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(x+sqrt(x^2+1)))
%Y A385369 Cf. A006228, A177698, A385343.
%K A385369 sign,easy
%O A385369 0,5
%A A385369 _Seiichi Manyama_, Jun 26 2025