A207835 G.f.: exp( Sum_{n>=1} 5*L(n)*x^n/n ), where L(n) = Fibonacci((n-1)^2) + Fibonacci((n+1)^2).

1, 15, 200, 3525, 134355, 16781664, 6730280105, 7679335074975, 23795707614699850, 197148338964056588955, 4337960355881995023988299, 252594793852565664429620014530, 38838042059493582778244565420563025, 15744729667082405326504405819215652913325

Offset: 0

Author

Paul D. Hanna, Feb 20 2012

Keywords

• nonn

Comments

Given g.f. A(x), note that A(x)^(1/5) is not an integer series.

Compare the definition to the g.f. of the Fibonacci numbers:

1/(1-x-x^2) = exp( Sum_{n>=1} Lucas(n)*x^n/n ), where Lucas(n) = Fibonacci(n-1) + Fibonacci(n+1).

Examples

			G.f.: A(x) = 1 + 15*x + 200*x^2 + 3525*x^3 + 134355*x^4 + 16781664*x^5 +...
such that, by definition,
log(A(x))/5 = 3*x + 35*x^2/2 + 990*x^3/3 + 75059*x^4/4 + 14931339*x^5/5 + 7778817074*x^6/6 +...+ (Fibonacci((n-1)^2) + Fibonacci((n+1)^2))*x^n/n +...
		

Crossrefs

Cf. A207834, A156216, A166168.

Programs

PARI

{L(n)=fibonacci((n-1)^2)+fibonacci((n+1)^2)}
{a(n)=polcoeff(exp(sum(m=1,n,5*L(m)*x^m/m)+x*O(x^n)),n)}
for(n=0,21,print1(a(n),", "))