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a_d = sum_{i+j=d} a_i*a_j ( i^2*j^2*binom(3d-4, 3i-2) - i^3*j*binom(3d-4, 3i-1) ).

a := proc(d:nonnegint) options remember; if d = 1 then 1 else sum('a(k)*a(d-k)*(k^2*(d-k)^2*binomial(3*d-4, 3*k-2)-k^3*(d-k)*binomial(3*d-4, 3*k-1))', 'k' = 1 .. d-1) fi end

(PARI) a(n)= if(n<2, n>0, sum(k=1, n-1, a(k)*a(n-k)*k^2*(n-k)*(3*k-n)*(3*n-4)!/(3*k-1)!/(3*(n-k)-2)! ))

Sequence in context: A159722 A042111 A159644 this_sequence A126159 A071307 A060612

Adjacent sequences: A013584 A013585 A013586 this_sequence A013588 A013589 A013590

nonn,easy,nice

Gary Kennedy (kennedy(AT)math.ohio-state.edu)

Additional terms and references from Michael Somos.