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Search: id:A105277
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| A105277 |
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Let b(n) denote the Fibonacci numbers, A000045: a(n) = Sum{k=0..n}C(n,k)^2*(n-k)!*b(k). |
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+0
2
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| 0, 1, 5, 29, 203, 1680, 16058, 173865, 2099957, 27952999, 406125305, 6389713034, 108157272720, 1958821525361, 37779732341077, 772829270394685, 16708083353842267, 380563529091632760, 9106983116342966818
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OFFSET
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0,3
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COMMENT
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If E.g.f. of b(n) is E(x) and a(n) = Sum{k=0..n}C(n,k)^2*(n-k)!*b(k), then E.g.f. of a(n) is E(x/(1-x))/(1-x).
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FORMULA
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E.g.f.: (2/sqrt(5))*exp(x/2/(1-x))*sinh(sqrt(5)*x/2/(1-x))/(1-x).
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EXAMPLE
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b(n) = 0,1,1,2,3,5,8,13,21,34,55,...
a(3) = C(3,0)^2*3!*b(0)+C(3,1)^2*2!*b(1)+C(3,2)^2*1!*b(2)+C(3,3)^2*0!*b(3) = 1*6*0+9*2*1+9*1*1+1*1*2 = 0+18+9+2 = 29
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MAPLE
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b[0]:=0:b[1]:=1:for n from 2 to 30 do b[n]:=b[n-1]+b[n-2] od: seq(sum('binomial(n, k)^2*(n-k)!*b[k]', 'k'=0..n), n=0..30);
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CROSSREFS
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Cf. A000045.
Adjacent sequences: A105274 A105275 A105276 this_sequence A105278 A105279 A105280
Sequence in context: A094710 A108453 A004213 this_sequence A103213 A057588 A030522
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Apr 25 2005
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