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 A381172 #10 Feb 16 2025 09:41:04
%S A381172 1,1,6,75,1416,36065,1160400,45182347,2066343552,108594342369,
%T A381172 6449557524480,427226389872491,31230489190382592,2497416890105693569,
%U A381172 216875134620623990784,20324880119519860657515,2044641793664946681446400,219762483007148574205773377,25134006030221243013604835328
%N A381172 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cosh(x * A(x)) ).
%C A381172 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381172 a(n) = Sum_{k=0..n} k! * binomial(n+2*k+1,k)/(n+2*k+1) * A185951(n,k).
%o A381172 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381172 a(n) = sum(k=0, n, k!*binomial(n+2*k+1, k)/(n+2*k+1)*a185951(n, k));
%Y A381172 Cf. A162654, A215364, A381171.
%Y A381172 Cf. A364984, A381175.
%Y A381172 Cf. A185951.
%K A381172 nonn
%O A381172 0,3
%A A381172 _Seiichi Manyama_, Feb 16 2025