A367030 G.f. satisfies A(x) = 1 + x*A(x) - x^2*A(x)^5.
1, 1, 0, -5, -15, 0, 170, 619, 69, -8351, -33601, -8446, 480679, 2078534, 830739, -30221481, -138791261, -76306831, 2009474129, 9742939809, 6811893809, -138835809721, -708398431831, -599833654686, 9861055840019, 52859680413599, 52446605719469
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, (-1)^k*binomial(n+3*k, k)*binomial(n+2*k, n-2*k)/(4*k+1));
Formula
a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+3*k,k) * binomial(n+2*k,n-2*k) / (4*k+1).