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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

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: 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 February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)