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PROGRAM
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(PARI)
(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])}
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