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Expansion 1/(1-x^2*cotan(x)) = Sum_{n>=0} a(n)*x^n/(n)!^2.
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%I #11 Dec 26 2023 09:39:59

%S 1,1,4,24,192,-320,-138240,-10214400,-669204480,-43782488064,

%T -2628064051200,-91419903590400,14288196206592000,5367226212019077120,

%U 1259862249808204922880,257126813359346810880000,46529454048255997378560000

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

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

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

%K sign

%O 0,3

%A _Vladimir Kruchinin_, Nov 07 2011