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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A249892 G.f.: Sum_{n>=0} x^n / (1 - n*x - n^2*x^2). 0
1, 1, 2, 5, 15, 52, 207, 923, 4532, 24271, 140581, 874434, 5806557, 40955973, 305544958, 2402139329, 19837601155, 171598571288, 1550865447043, 14611295961047, 143210242799872, 1457573997373131, 15379106145570681, 167962044452359398, 1896100883094424657, 22096376018936592193 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

From Vaclav Kotesovec, Nov 09 2014: (Start)

(a(n))^(1/n) ~ phi^(1-1/w) * n^(1-1/w) / w^(1-1/w), where w = LambertW(phi*e*n).

Limit n->infinity a(n)^(1/n) * LambertW(phi*e*n) / n = phi/e, where phi = (1+sqrt(5))/2 = A001622.

(End)

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = Sum_{k=0..n} Fibonacci(n-k+1) * k^(n-k).

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 52*x^5 + 207*x^6 +...

where

A(x) = 1 + x/(1-x-x^2) + x^2/(1-2*x-4*x^2) + x^3/(1-3*x-9*x^2) + x^4/(1-4*x-16*x^2) +  x^5/(1-5*x-25*x^2) + x^6/(1-6*x-36*x^2) + x^7/(1-7*x-49*x^2) +...

MATHEMATICA

Flatten[{1, Table[Sum[Fibonacci[n-k+1] * k^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Nov 09 2014 *)

PROG

(PARI) {a(n)=polcoeff((sum(m=0, n, x^m/(1-m*x-m^2*x^2 +x*O(x^n)))), n)}

for(n=0, 30, print1(a(n), ", "))

(PARI) {a(n)=sum(k=0, n, fibonacci(n-k+1)*k^(n-k))}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A000045.

Sequence in context: A186001 A134381 A107589 * A006790 A007548 A328431

Adjacent sequences:  A249889 A249890 A249891 * A249893 A249894 A249895

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 08 2014

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 November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)