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Search: id:A130406
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| 1, 3, 13, 83, 814, 12502, 303102, 11681388, 718217460, 70660085940, 11145552305760, 2823029266531680, 1149529177121700960, 753213189796615454400, 794745942920930023732800
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = F(n+2)*a(n-1) + F(n+1)*A003266(n+1), where A003266(n) is the product of the first n nonzero Fibonacci numbers (A000045) and F(n) = A000045(n).
a(n) = A003266(n+1)*[ F(n+1) + F(n+2)*Sum_{k=0..n} F(k)/F(k+1) ] where F(n)=A000045(n) is the n-th Fibonacci number.
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EXAMPLE
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a(n) = A003266(n+1)*[F(n+1) + F(n+2)*[1+ 1/2+ 2/3+ 3/5+...+ F(n)/F(n+1)]]:
a(3) = 1*1*2*3*( 3 + 5*(1/1 + 1/2 + 2/3) ) = 83;
a(4) = 1*1*2*3*5*( 5 + 8*(1/1 + 1/2 + 2/3 + 3/5) ) = 814;
a(5) = 1*1*2*3*5*8*( 8 + 13*(1/1 + 1/2 + 2/3 + 3/5 + 5/8) ) = 12502.
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PROGRAM
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(PARI) {a(n)=polcoeff(prod(i=0, n+1, fibonacci(i+1)+x*fibonacci(i)), 1)} (PARI) /* Recurrence a(n) = F(n+2)*a(n-1) + F(n+1)*A003266(n+1): */ {a(n)=if(n==0, 1, fibonacci(n+2)*a(n-1)+fibonacci(n+1)*prod(i=1, n+1, fibonacci(i)))}
(PARI) {a(n)=prod(i=1, n+1, fibonacci(i))*(fibonacci(n+1) + fibonacci(n+2)*sum(k=0, n, fibonacci(k)/fibonacci(k+1)))}
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CROSSREFS
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Cf. A130405, A130407; A003266, A000045.
Sequence in context: A135743 A123114 A104032 this_sequence A125500 A121679 A023037
Adjacent sequences: A130403 A130404 A130405 this_sequence A130407 A130408 A130409
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 24 2007, May 25 2007
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