A168595 a(n) = Sum_{k=0..2n} C(2n,k)*A027907(n,k) where A027907 is the triangle of trinomial coefficients.

1, 4, 36, 358, 3748, 40404, 443886, 4941654, 55555236, 629285416, 7170731236, 82108083204, 943960439086, 10889085499348, 125974782200478, 1461030555025458, 16981658850393252, 197757344280343968

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

Table of n, a(n) for n=0..17.

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: A026334 A247562 A372465 * A163455 A371772 A138736

Adjacent sequences: A168592 A168593 A168594 * A168596 A168597 A168598

Keyword

nonn

Author

Paul D. Hanna, Nov 30 2009

Status

approved