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A000557
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From Fibonacci sums.
(Formerly M1881 N0743)
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5
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1, 2, 8, 50, 416, 4322, 53888, 783890, 13031936, 243733442, 5064992768, 115780447730, 2887222009856, 77998677862562, 2269232452763648, 70734934220015570, 2351893466832306176, 83086463910558199682, 3107896091715557654528, 122711086194279627711410
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. Ledin, On a certain kind of Fibonacci sums, Fib. Quart., 5 (1967), 45-58.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| E.g.f.: 1/(1-2*sinh(x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 06 2002
a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^j*binomial(k,j)*(k-2*j)^n. [Peter Luschny, Jul 31 2011]
a(n) = Sum[k=0..n, k!*Stirling2(n, k)*Fibonacci(k+2)].
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MAPLE
| A000557 := proc(n) local k, j; add(add((-1)^j*binomial(k, j)*(k-2*j)^n, j=0..k), k=0..n) end: [Peter Luschny, Jul 31 2011]
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MATHEMATICA
| f[n_] := Sum[ k!*StirlingS2[n, k]*Fibonacci[k + 2], {k, 0, n}]; Array[f, 20, 0] (* Robert G. Wilson v, Aug 16 2011 *)
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CROSSREFS
| Sequence in context: A186182 A121677 A120956 * A193352 A002801 A089104
Adjacent sequences: A000554 A000555 A000556 * A000558 A000559 A000560
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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