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A093131
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Binomial transform of Fib(2n).
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5
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0, 1, 5, 20, 75, 275, 1000, 3625, 13125, 47500, 171875, 621875, 2250000, 8140625, 29453125, 106562500, 385546875, 1394921875, 5046875000, 18259765625, 66064453125, 239023437500, 864794921875, 3128857421875, 11320312500000
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OFFSET
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0,3
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COMMENTS
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Second binomial transform of Fib(n). - Paul Barry, Apr 22 2005
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REFERENCES
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M. Griffiths, Families of Sequences From a Class of Multinomial Sums, Journal of Integer Sequences, 15 (2012), #12.1.8.
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LINKS
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Table of n, a(n) for n=0..24.
Index to sequences with linear recurrences with constant coefficients, signature (5,-5).
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FORMULA
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G.f.: x/(1-5x+5x^2); a(n)=(((5+sqrt(5))/2)^n-((5-sqrt(5))/2)^n)/sqrt(5); a(n)=A093130(n)/2^n.
a(n)=sum{k=0..n, sum{j=0..n, C(n, j)C(j, k)F(j-k)}}; - Paul Barry, Feb 15 2005
a(n)=sum{k=0..n, C(n, k)F(n-k)2^k}=sum{k=0..n, C(n, k)F(k)2^(n-k)}; - Paul Barry, Apr 22 2005
a(n)=A030191(n-1), n>0. [From R. J. Mathar, Sep 05 2008]
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CROSSREFS
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Cf. A030191, A000045.
Sequence in context: A022633 A092490 A094828 * A030191 A224422 A000344
Adjacent sequences: A093128 A093129 A093130 * A093132 A093133 A093134
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Mar 23 2004
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STATUS
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approved
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