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 A381445 #10 Feb 24 2025 05:37:07
%S A381445 1,1,6,75,1392,34925,1108080,42562807,1920796416,99628495353,
%T A381445 5840628226560,381927689957891,27562916396961792,2176123474607538469,
%U A381445 186580455503952427008,17264834430223073672175,1714909152672462179205120,182002038900785304200753777,20553746198157175799599202304
%N A381445 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x) * A(x)^2 ).
%C A381445 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381445 a(n) = Sum_{k=0..n} k! * binomial(3*k+1,k)/(3*k+1) * A185951(n,k).
%o A381445 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381445 a(n) = sum(k=0, n, k!*binomial(3*k+1, k)/(3*k+1)*a185951(n, k));
%Y A381445 Cf. A205571, A295256, A381446.
%Y A381445 Cf. A185951.
%K A381445 nonn
%O A381445 0,3
%A A381445 _Seiichi Manyama_, Feb 23 2025