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 A381477 #8 Feb 25 2025 06:43:56
%S A381477 1,1,6,75,1440,37445,1231440,49037527,2294425728,123393443049,
%T A381477 7500623201280,508577491719011,38057966976387072,3115680296111519149,
%U A381477 277005128553759191040,26579020362900758232495,2737628961211699538657280,301278578823933606439917137,35281158151116225085977526272
%N A381477 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cosh(x * A(x)^2) ).
%C A381477 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381477 a(n) = Sum_{k=0..n} k! * binomial(2*n+k+1,k)/(2*n+k+1) * A185951(n,k).
%F A381477 E.g.f.: ( (1/x) * Series_Reversion( x*(1 - x*cosh(x))^2 ) )^(1/2).
%o A381477 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381477 a(n) = sum(k=0, n, k!*binomial(2*n+k+1, k)/(2*n+k+1)*a185951(n, k));
%Y A381477 Cf. A185951, A364985, A381386.
%K A381477 nonn
%O A381477 0,3
%A A381477 _Seiichi Manyama_, Feb 24 2025