A200539 Product of Fibonacci and Motzkin numbers: a(n) = A000045(n+1)*A001006(n).

1, 1, 4, 12, 45, 168, 663, 2667, 10982, 45925, 194732, 834912, 3614063, 15771795, 69316740, 306534564, 1362986799, 6089916936, 27328613142, 123118156260, 556626199974, 2524659817449, 11484671681511, 52384730922720, 239534402969925, 1097805759803893, 5042014405418968

Offset: 0

Author

Paul D. Hanna, Nov 18 2011

Keywords

• nonn

Comments

The g.f. for the Fibonacci numbers is 1/(1-x-x^2) and the g.f. M(x) for the Motzkin numbers satisfies: M(x) = 1 + x*M(x) + x^2*M(x)^2.

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 12*x^3 + 45*x^4 + 168*x^5 + 663*x^6 +...
where A(x) = 1*1 + 1*1*x + 2*2*x^2 + 3*4*x^3 + 5*9*x^4 + 8*21*x^5 + 13*51*x^6 + 21*127*x^7 + 34*323*x^8 +...+ A000045(n+1)*A001006(n)*x^n +...
		

Crossrefs

Cf. A098614, A200538, A200540, A098616.

Programs

PARI

{A001006(n)=polcoeff((1-x-sqrt((1-x)^2-4*x^2+x^3*O(x^n)))/(2*x^2),n)}
{a(n)=fibonacci(n+1)*A001006(n)}