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Column 0 of triangle A107719.
1

%I #6 Jul 03 2018 05:06:41

%S 1,1,5,43,509,7579,135341,2813851,66733853,1778159275,52604224205,

%T 1711276244731,60729274013309,2335153500391627,96727188777453869,

%U 4294441686826824091,203456100846249179357,10245810557884742785387

%N Column 0 of triangle A107719.

%o (PARI) {a(n)=local(E,L,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-3*j, -polcoeff(1-(1+sum(c=1,m-j,prod(i=0,c-1,3*i+1)*x^c)+x*O(x^(m-j)))^-1,m-j);))))^-1); L=matrix(#M,#M,r,c,if(r>=c,sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i)[r,c])); E=matrix(#L,#L,r,c,if(r>=c,sum(i=0,#L,L^i/3^i/i!)[r,c])); if(n<0,0,E[n+1,1])}

%Y Cf. A107717, A107719.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 30 2005