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 A207835 G.f.: exp( Sum_{n>=1} 5*L(n)*x^n/n ), where L(n) = Fibonacci((n-1)^2) + Fibonacci((n+1)^2). 4
 1, 15, 200, 3525, 134355, 16781664, 6730280105, 7679335074975, 23795707614699850, 197148338964056588955, 4337960355881995023988299, 252594793852565664429620014530, 38838042059493582778244565420563025, 15744729667082405326504405819215652913325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). LINKS EXAMPLE 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 +... PROG (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), ", ")) CROSSREFS Cf. A207834, A156216, A166168. Sequence in context: A014896 A048444 A002007 * A178507 A012566 A238992 Adjacent sequences:  A207832 A207833 A207834 * A207836 A207837 A207838 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 20 2012 STATUS approved

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Last modified April 10 02:20 EDT 2020. Contains 333392 sequences. (Running on oeis4.)