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%I #4 Jun 13 2015 09:39:50
%S 1,-6,85,-1350,26341,-603246,15887845,-473148150,15723174181,
%T -576826897086,23157022930405,-1009818279438150,47533643556874021,
%U -2402218856253008526,129730266330534913765,-7455932648513351731350,454377365410347843373861
%N Column 3 of triangle A136595.
%F a(n) = Sum_{i=0..n-1} (-1)^i*(3+i)!*Stirling2(n,3+i)*Catalan(3,i)/3!, where Stirling2(n,k) = A008277(n,k), Catalan(k,i) = C(2*i+k,i)*k/(2*i+k) = coefficient of x^i in C(x)^k with C(x) = (1-sqrt(1-4x))/(2x).
%o (PARI) a(n)=n!/2!* sum(i=0,n-1,(-1)^i*polcoeff(((exp(x+x*O(x^n))-1)^(3+i)),n)*binomial(2*i+3,i)/(2*i+3))
%o (PARI) /* Define Stirling2: */ {Stirling2(n,k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!,n)} /* Define Catalan(m,n) = [x^n] C(x)^m: */ {Catalan(m,n)=binomial(2*n+m,n)*m/(2*n+m)} /* Define this sequence: */ {a(n)=sum(i=0,n-1,(-1)^i*(3+i)!*Stirling2(n,3+i)*Catalan(3,i)/3!)}
%Y Cf. A136595, A048287, A136596.
%K sign
%O 3,2
%A _Paul D. Hanna_, Jan 10 2008
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