login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005445 From a Fibonacci-like differential equation.
(Formerly M4487)
1
0, 1, 1, 8, 16, 224, 608, 13320, 41760, 1366152, 4440312, 215100192, 655723440, 48242081328, 121651212720, 14627299801728, 24367884018048, 5768946415383552, 2780730890516736, 2872938805170308352, -2941729703083507968, 1764460446550873413120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..21.

P. R. J. Asveld & N. J. A. Sloane, Correspondence, 1987

P. R. J. Asveld, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309.

FORMULA

E.g.f.: log(1+x)/(1-log(1+x)-log(1+x)^2). a(n) = Sum_{k=0..n} Stirling1(n, k)*k!*Fibonacci(k). - Vladeta Jovovic, Sep 29 2003

a(n) ~ n! * (-1)^(n+1) * (1+1/sqrt(5)) * exp(n*(1+sqrt(5))/2) /(2*(exp((1+sqrt(5))/2)-1)^(n+1)). - Vaclav Kotesovec, Oct 01 2013

MATHEMATICA

CoefficientList[Series[Log[1+x]/(1-Log[1+x]-(Log[1+x])^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)

PROG

(PARI) a(n) = sum(k=0, n, k!*fibonacci(k)*stirling(n, k, 1)); \\ Michel Marcus, Oct 30 2015

CROSSREFS

Sequence in context: A061359 A330150 A340586 * A322342 A132377 A276978

Adjacent sequences:  A005442 A005443 A005444 * A005446 A005447 A005448

KEYWORD

sign

AUTHOR

Simon Plouffe

EXTENSIONS

More terms from Vladeta Jovovic, Sep 29 2003

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)