login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000557 From Fibonacci sums.
(Formerly M1881 N0743)
7
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; text; internal format)
OFFSET

0,2

COMMENTS

Inverse binomial transform of A005923. - Vladimir Reshetnikov, Oct 29 2015

REFERENCES

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).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

G. Ledin, Jr., On a certain kind of Fibonacci sums, Fib. Quart., 5 (1967), 45-58.

Eric Weisstein's MathWorld, Polylogarithm.

FORMULA

E.g.f.: 1/(1-2*sinh(x)). - Vladeta Jovovic, 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).

a(n) ~ n! / (sqrt(5) * log((1+sqrt(5))/2)^(n+1)). - Vaclav Kotesovec, May 04 2015

a(n) = (-1)^n*(Li_{-n}(1-phi)-Li_{-n}(phi))/sqrt(5), where Li_n(x) denotes the polylogarithm, phi=(1+sqrt(5))/2. - Vladimir Reshetnikov, Oct 29 2015

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

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 *)

With[{nn=20}, CoefficientList[Series[1/(1-2*Sinh[x]), {x, 0, nn}], x]Range[ 0, nn]!] (* Harvey P. Dale, Mar 11 2012 *)

Round@Table[(-1)^n (PolyLog[-n, 1-GoldenRatio]-PolyLog[-n, GoldenRatio])/Sqrt[5], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 29 2015 *)

CROSSREFS

Cf. A000045, A005923.

Sequence in context: A274273 A121677 A120956 * A193352 A002801 A233436

Adjacent sequences:  A000554 A000555 A000556 * A000558 A000559 A000560

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 05:09 EDT 2017. Contains 292502 sequences.