A381300 - OEIS

%I #8 Feb 20 2025 08:39:24

%S 1,1,2,9,60,485,4800,57547,804160,12783969,228447360,4539156941,

%T 99244045824,2367795157741,61230675251200,1706241143585175,

%U 50971847057326080,1625178125581055297,55087299146009640960,1978201530490562626609,75025096312729021972480

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

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

%F a(n) = Sum_{k=0..n} k! * binomial(n/2+k/2+1,k)/(n/2+k/2+1) * 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) = sum(k=0, n, k!*binomial(n/2+k/2+1, k)/(n/2+k/2+1)*a185951(n, k));

%Y Cf. A185951.

%K nonn,new

%O 0,3

%A _Seiichi Manyama_, Feb 19 2025