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 A381310 #8 Feb 20 2025 08:40:02
%S A381310 1,1,1,0,-7,-38,-111,259,7025,59752,209297,-2545257,-59541487,
%T A381310 -609139048,-1257456543,86370090271,1968628674465,20998208227456,
%U A381310 -60103780767519,-7806917233342465,-175430347192682527,-1683391495632464904,26661441929560502097,1550891419460475900175
%N A381310 E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^(1/2)) / A(x)^(1/2) ).
%F A381310 a(n) = Sum_{k=0..n} (n/2-k/2+1)^(k-1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381310 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381310 a(n) = sum(k=0, n, (n/2-k/2+1)^(k-1)*I^(n-k)*a136630(n, k));
%Y A381310 Cf. A136630.
%K A381310 sign
%O A381310 0,5
%A A381310 _Seiichi Manyama_, Feb 19 2025