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A090162
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Values of binomial(Fibonacci(2k)*Fibonacci(2k+1),Fibonacci(2k-1)*Fibonacci(2k)-1).
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7
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OFFSET
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1,2
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COMMENTS
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These numbers are known to occur at least six times in Pascal's triangle.
The next term is approximately 3.537 * 10^204 and is in the b-file.
The numbers of digits in a(n), n >= 1, are given in A100022.
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LINKS
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FORMULA
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MAPLE
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a := proc(n) local a, b, s, p; s:= 1+sqrt(5); p:=16^n;
a := 4-2*p*s^(-4*n-1)+(s+2)*s^(4*n-1)/p:
b := 1+p*((s-2)^(1-4*n)/2-s^(-1-4*n)*(2+s)):
GAMMA(a/5)/(GAMMA(b/5)*GAMMA(1+(a-b)/5)) end:
digits := [1, 4, 29, 205, 1412]: A := n -> round(evalf(a(n), digits[n]+10)):
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MATHEMATICA
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Table[Binomial[Fibonacci[2k]Fibonacci[2k+1], Fibonacci[2k-1] Fibonacci[2k]-1], {k, 4}] (* Harvey P. Dale, Aug 18 2011 *)
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PROG
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(PARI) A090162(n)=binomial(fibonacci(2*n+1)*fibonacci(2*n), fibonacci(2*n-1)*fibonacci(2*n)-1) \\ M. F. Hasler, Feb 17 2023
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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