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%I #15 Aug 25 2019 17:47:57
%S 1,1,2,-6,-168,-2600,-10800,727440,43263360,1032103296,-228614400,
%T -3068098387200,-194799891686400,-9157262446126080,406734380101969920,
%U 68528048007234816000,9942165414475886592000,179947145139068340633600,-678953675518129505894400
%N a(n) is defined by exp(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)!)))))/m!), a(0)=1.
%e exp(x^2*cot(x)) = 1+x+(1/2)*x^2-(1/6)*x^3-(7/24)*x^4-(13/72)*x^5-(1/48)*x^6+(433/15120)*x^7+(1073/40320)*x^8+(14221/1814400)*x^9-(1/57600)*x^10-...
%p t1 := exp(x^2*cot(x));
%p t2 := series(t1,x,21);
%p t3 := seriestolist(t2);
%p t4 := [seq(t3[n]*(n-1)!^2,n=1..nops(t3))]; # _N. J. A. Sloane_, Aug 25 2019
%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!, m,1,n);
%K sign
%O 0,3
%A _Vladimir Kruchinin_, Nov 06 2011
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