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 A380050 #11 Jan 11 2025 10:26:32
%S A380050 1,1,3,9,25,25,-429,-4151,-8175,320625,5241475,23329801,-705579159,
%T A380050 -18521117303,-150119840493,3366485315145,138253031778721,
%U A380050 1780881865542625,-28047359274759549,-1854674541474191351,-34985197604145203655,332608115115937927161
%N A380050 E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*exp(x)*A(x) ).
%F A380050 E.g.f.: exp( arcsinh(x*exp(x)) ).
%F A380050 E.g.f.: x*exp(x) + sqrt(1 + x^2*exp(2*x)).
%F A380050 a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(k/2+1/2,k)/( (k+1)*(n-k)! ).
%o A380050 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(asinh(x*exp(x)))))
%o A380050 (PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(k/2+1/2, k)/((k+1)*(n-k)!));
%Y A380050 Cf. A006153, A380051.
%Y A380050 Cf. A297010, A380044.
%K A380050 sign
%O A380050 0,3
%A A380050 _Seiichi Manyama_, Jan 11 2025