A157143 A transform of the Motzkin numbers.

1, -1, -1, 0, 2, 1, -1, -4, -2, 5, 11, 0, -21, -24, 18, 68, 42, -100, -203, -17, 428, 521, -340, -1544, -1019, 2252, 4892, 606, -10297, -13331, 7821, 39310, 28028, -56893, -130394, -22239, 272991, 370641, -193874, -1081694, -821669, 1536026, 3707766, 798376

Offset

0,5

Comments

Hankel transform is A157144.

Links

Table of n, a(n) for n=0..43.

Formula

G.f.: (1-x)/(1+x^2+x^3)*c((x/(1+x^2+x^3))^2), c(x) the g.f. of A000108. - (The formula does not match the entries, even if A000108 is replaced by A001006. R. J. Mathar, Feb 06 2015)

a(n)=sum{k=0..n, (-1)^C(n-k+1,2)*C(floor((n-k)/2),k)*A001006(k)}.

Prog

(PARI) A157143(n)=vector(n++, k, (-1)^binomial(n+1-k, 2)*binomial((n-k)\2, k-1))*Vec(serreverse(x/(1+x+x^2+O(x^n))))~ \\ M. F. Hasler, Feb 09 2015

Crossrefs

Cf. A001006.

Sequence in context: A346032 A157125 A335941 * A112096 A217874 A323182

Adjacent sequences: A157140 A157141 A157142 * A157144 A157145 A157146

Keyword

easy,sign

Author

Paul Barry, Feb 24 2009

Status

approved