A385251 a(n) = Sum_{k=0..n-1} binomial(4*k-3,k) * binomial(4*n-4*k,n-k-1).
0, 1, 9, 84, 790, 7452, 70401, 665692, 6298236, 59612556, 564393460, 5344664400, 50621130078, 479513718116, 4542730477758, 43039907282664, 407809863233592, 3864303038901996, 36619104142640460, 347027703183853552, 3288802989845088504, 31169274939274755312
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n-1, binomial(4*k-3, k)*binomial(4*n-4*k, n-k-1));
Formula
G.f.: (g-1)/(g * (4-3*g)^2) where g=1+x*g^4.
G.f.: g * (1-g)^2/(1-4*g)^2 where g*(1-g)^3 = x.
a(n) = Sum_{k=0..n-1} binomial(4*k-3+l,k) * binomial(4*n-4*k-l,n-k-1) for every real number l.
a(n) = Sum_{k=0..n-1} 3^(n-k-1) * binomial(4*n-2,k).
a(n) = Sum_{k=0..n-1} 4^(n-k-1) * binomial(3*n+k-2,k).