A163189 G.f.: A(x) = exp( Sum_{n>=1} (1 + A000204(n)*x)^n * x^n/n ).

1, 1, 2, 5, 14, 40, 159, 812, 5133, 42942, 474619, 6708142, 121367878, 2819170132, 83571532538, 3148951107867, 151069353323782, 9219463980803329, 714951048370178409, 70448496563603216429, 8818161368662624534857

Offset

0,3

Comments

Compare to g.f. of Fibonacci sequence: exp( Sum_{n>=1} A000204(n)*x^n/n ), where A000204 is the Lucas numbers.

Links

Table of n, a(n) for n=0..20.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 159*x^6 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (1+(fibonacci(m-1)+fibonacci(m+1))*x+x*O(x^n))^m*x^m/m)), n)}

Crossrefs

Cf. A156216, A156100, A159308, A000204.

Sequence in context: A148321 A007463 A159308 * A243881 A358416 A225691

Adjacent sequences: A163186 A163187 A163188 * A163190 A163191 A163192

Keyword

nonn

Author

Paul D. Hanna, Jul 22 2009

Status

approved