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A168595
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a(n) = Sum_{k=0..2n} C(2n,k)*A027907(n,k) where A027907 is the triangle of trinomial coefficients.
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4
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1, 4, 36, 358, 3748, 40404, 443886, 4941654, 55555236, 629285416, 7170731236, 82108083204, 943960439086, 10889085499348, 125974782200478, 1461030555025458, 16981658850393252, 197757344280343968
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OFFSET
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0,2
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COMMENTS
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Compare to A092765(n) = Sum_{k=0..2n} (-1)^k*C(2n,k)*A027907(n,k), which is the number of paths of length n ending at origin in 1-D random walk with jumps to next-nearest neighbors.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*cb(n+k) with cb(n) = binomial(2n,n). - Peter Luschny, Aug 15 2017
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MAPLE
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cb := n -> binomial(2*n, n);
a := n -> add((-1)^(n-k)*binomial(n, k)*cb(n+k), k=0..n);
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PROG
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(PARI) {a(n)=sum(k=0, 2*n, binomial(2*n, k)*polcoeff((1+x+x^2)^n, k))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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