A090162 Values of binomial(Fibonacci(2k)*Fibonacci(2k+1),Fibonacci(2k-1)*Fibonacci(2k)-1).
1, 3003, 61218182743304701891431482520
Offset: 1
Links
- Hugo Pfoertner, Table of n, a(n) for n = 1..5
- A. I. Shirshov, On the equation C(n, m) = C(n+1, m-1), chapter 10 in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, Am. Math. Soc., 1999, pp. 83-86
- D. Singmaster, Repeated binomial coefficients and Fibonacci numbers, Fibonacci Quarterly, 13 (1975), 295-298.
- Eric Weisstein's World of Mathematics, Pascal's Triangle
Programs
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Maple
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)): A(4); # Peter Luschny, Jul 15 2017
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Mathematica
Table[Binomial[Fibonacci[2k]Fibonacci[2k+1],Fibonacci[2k-1] Fibonacci[2k]-1], {k,4}] (* Harvey P. Dale, Aug 18 2011 *) -
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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Python
def A090162(n): return C(A000045(2*n+1)*A000045(2*n),A000045(2*n-1)*A000045(2*n)-1) # See A007318 for C(.,.). - M. F. Hasler, Feb 17 2023
Comments