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 A381306 #9 Feb 20 2025 08:39:45
%S A381306 1,1,2,5,12,1,-416,-5741,-60800,-543719,-3479424,6260561,822338048,
%T A381306 20933340065,393396789248,5840683299431,54344509046784,
%U A381306 -481407806103119,-44548560374988800,-1564969488082711811,-40856692743724335104,-812774967576805701599,-8614414458975040831488
%N A381306 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^(1/2)) / A(x)^(1/2) ).
%F A381306 a(n) = Sum_{k=0..n} k! * binomial(n/2+k/2+1,k)/(n/2+k/2+1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381306 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381306 a(n) = sum(k=0, n, k!*binomial(n/2+k/2+1, k)/(n/2+k/2+1)*I^(n-k)*a136630(n, k));
%Y A381306 Cf. A136630.
%K A381306 sign
%O A381306 0,3
%A A381306 _Seiichi Manyama_, Feb 19 2025