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 A168595 a(n) = Sum_{k=0..2n} C(2n,k)*A027907(n,k) where A027907 is the triangle of trinomial coefficients. 4
 1, 4, 36, 358, 3748, 40404, 443886, 4941654, 55555236, 629285416, 7170731236, 82108083204, 943960439086, 10889085499348, 125974782200478, 1461030555025458, 16981658850393252, 197757344280343968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS FORMULA a(n) = 2*A132306(n) for n > 0. - Mark van Hoeij, Jul 02 2010 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 MAPLE cb := n -> binomial(2*n, n); a := n -> add((-1)^(n-k)*binomial(n, k)*cb(n+k), k=0..n); seq(a(n), n=0..17); # Peter Luschny, Aug 15 2017 PROG (PARI) {a(n)=sum(k=0, 2*n, binomial(2*n, k)*polcoeff((1+x+x^2)^n, k))} CROSSREFS Cf. A027907, A092765. Sequence in context: A189334 A026334 A247562 * A163455 A138736 A266093 Adjacent sequences:  A168592 A168593 A168594 * A168596 A168597 A168598 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 30 2009 STATUS approved

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Last modified January 22 01:33 EST 2019. Contains 319351 sequences. (Running on oeis4.)