%I #14 Dec 26 2023 09:39:37

%S 1,1,4,30,384,7480,207360,7780080,380190720,23481311616,1789201612800,

%T 164904696633600,18084647927808000,2327418985883397120,

%U 347368297708734382080,59514548453599599360000,11601363342443780505600000,2552998389393196650531225600

%N Expansion 1/(1-x^2*cosech(x)) = Sum_{n>=0} a(n)*x^n/n!^2.

%F a(n) = n!^2*sum(m=1..n, m!*sum(i=0..n-m, (2^i*m^(n-m-i)* sum(k=0..i, (stirling2(i,k)*k!*stirling1(m+k,m))/(m+k)!))/(i!*(n-m-i)!))), n>0, a(0)=1.

%e 1/(1-x^2*csch(x)) = 1 + x + x^2 + (5*x^3)/6 + (2*x^4)/3 + (187*x^5)/360 + (2*x^6)/5 + (4631*x^7)/1512 + (221*x^8)/945 + (11983*x^9)/67200 + (214*x^10)/1575 + ...

%o (Maxima) a(n) := if n=0 then 1 else n!^2 * sum(m!*sum((2^i*m^(n-m-i)* sum((stirling2(i,k)*k!*stirling1(m+k,m))/(m+k)!,k,0,i))/(i!*(n-m-i)!),i,0,n-m),m,1,n)

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Nov 08 2011