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!)
A308940 Expansion of e.g.f. 1 / (1 - Sum_{k>=1} Fibonacci(k)*x^k/k!). 0
1, 1, 3, 14, 85, 645, 5878, 62495, 759351, 10379878, 157652085, 2633903669, 48005235886, 947849607015, 20154635314591, 459170181891230, 11158379672316837, 288109467764819749, 7876576756719778854, 227299554620022188879, 6904560742996004248135 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

E.g.f.: sqrt(5)/(sqrt(5) - 2*exp(x/2)*sinh(sqrt(5)*x/2)).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * Fibonacci(k) * a(n-k).

a(n) ~ n! * 5^((n+1)/2) * (exp(2*r) - 1) / ((sqrt(5) - 1 + (1 + sqrt(5))*exp(2*r)) * 2^n * r^(n+1)), where r = 0.7361181605960590527095268838693519750655284224... is the root of the equation exp(2*r) = 1 + sqrt(5)*exp(r*(1 - 1/sqrt(5))). - Vaclav Kotesovec, Jul 01 2019

MATHEMATICA

nmax = 20; CoefficientList[Series[Sqrt[5]/(Sqrt[5] - 2 Exp[x/2] Sinh[Sqrt[5] x/2]), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Fibonacci[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A000045, A097597, A215928.

Sequence in context: A331608 A331615 A317060 * A276313 A074520 A127715

Adjacent sequences:  A308937 A308938 A308939 * A308941 A308942 A308943

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 01 2019

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 May 12 09:53 EDT 2021. Contains 343821 sequences. (Running on oeis4.)