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A219462
a(n) = Sum_{k = 1..2*n} binomial(2*n,k) * Fibonacci(2*k).
1
0, 5, 75, 1000, 13125, 171875, 2250000, 29453125, 385546875, 5046875000, 66064453125, 864794921875, 11320312500000, 148184814453125, 1939764404296875, 25391845703125000, 332383575439453125, 4350957489013671875, 56954772949218750000, 745547657012939453125
OFFSET
0,2
FORMULA
a(n) = Sum_{k=1..n} A034870(n,k)*A001906(k).
a(n) = 5^n * Fibonacci(2*n) = A000351(n) * A001906(n).
G.f.: 5*x/(25*x^2-15*x+1). - Colin Barker, Dec 03 2012
E.g.f.: 2*exp(15*x/2)*sinh(5*sqrt(5)*x/2)/sqrt(5). - Stefano Spezia, Oct 19 2023
MATHEMATICA
Table[Sum[Binomial[2n, k]Fibonacci[2k], {k, 2n}], {n, 0, 20}] (* Harvey P. Dale, Aug 26 2017 *)
PROG
(Haskell)
a219462 = sum . zipWith (*) a001906_list . a034870_row
(PARI) a(n) = sum(k = 1, 2*n, binomial(2*n, k) * fibonacci(2*k)); \\ Michel Marcus, Jan 26 2022
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Nov 20 2012
STATUS
approved