A381377 - OEIS

%I #10 Feb 22 2025 09:56:23

%S 1,2,6,30,288,4090,68160,1292774,28627200,739821618,21729070080,

%T 708442911022,25365382259712,992297344710698,42173572623716352,

%U 1934344590577340790,95175474351245230080,5000227637170108004194,279428527333796676894720,16552583621200571079876158

%N E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)) )^2.

%C As stated in the comment of A185951, A185951(n,0) = 0^n.

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381376.

%F a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n-k+2,k)/(2*n-k+2) * A185951(n,k).

%o (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));

%o a(n) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*a185951(n, k));

%Y Cf. A185951, A381206, A381376.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Feb 22 2025