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 A385428 #15 Jun 28 2025 10:02:11
%S A385428 1,1,1,0,-11,-80,-219,3416,68265,550656,-3285975,-194101248,
%T A385428 -3177823395,-5431320960,1202586098637,35658624599040,359507959906641,
%U A385428 -12186663090266112,-677861502762897711,-13768767870225444864,126162451289700276165,19553934035547470168064
%N A385428 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)) / A(x) ).
%F A385428 E.g.f. A(x) satisfies A(x) = ( x*A(x) + sqrt((x*A(x))^2 + 1) )^(1/A(x)).
%F A385428 a(n) = Sum_{k=0..n} (n-k+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.
%o A385428 (PARI) a385343(n, k) = my(x='x+O('x^(n+1))); n!*polcoef(asin(x)^k/k!, n);
%o A385428 a(n) = sum(k=0, n, (n-k+1)^(k-1)*I^(n-k)*a385343(n, k));
%Y A385428 Cf. A001147, A385425.
%Y A385428 Cf. A381147, A385343, A385369.
%K A385428 sign
%O A385428 0,5
%A A385428 _Seiichi Manyama_, Jun 28 2025