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A023607 a(n) = n * Fibonacci(n+1).

%I A023607 #67 May 07 2025 09:03:23
%S A023607 0,1,4,9,20,40,78,147,272,495,890,1584,2796,4901,8540,14805,25552,
%T A023607 43928,75258,128535,218920,371931,630454,1066464,1800600,3034825,
%U A023607 5106868,8580897,14398412,24129160,40388070,67527579,112786496,188195271
%N A023607 a(n) = n * Fibonacci(n+1).
%C A023607 Convolution of Fibonacci numbers and Lucas numbers.
%C A023607 Central terms of the triangle in A119457 for n>0. - _Reinhard Zumkeller_, May 20 2006
%C A023607 d/dx(1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + ...) = (1 + 4x + 9x^2 + ...). - _Gary W. Adamson_, Jun 27 2009
%C A023607 For n > 0: sums of rows of the triangle in A108035. - _Reinhard Zumkeller_, Oct 08 2012
%H A023607 Reinhard Zumkeller, <a href="/A023607/b023607.txt">Table of n, a(n) for n = 0..1000</a>
%H A023607 M. Griffiths, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Griffiths/griffiths16.html">A Restricted Random Walk defined via a Fibonacci Process</a>, Journal of Integer Sequences, Vol. 14 (2011), #11.5.4.
%H A023607 Milan Janjić, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Janjic/janjic33.html">Hessenberg Matrices and Integer Sequences</a>, J. Int. Seq. 13 (2010) # 10.7.8, section 3.
%H A023607 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1).
%F A023607 O.g.f.: x(2x+1)/(1-x-x^2)^2. - _Len Smiley_, Dec 11 2001
%F A023607 a(n) = n*Sum_{k=0..n} binomial(k,n-k). - _Paul Barry_, Sep 25 2004
%F A023607 a(n) = A215082(2n-2) + A215082(2n-1). - _Philippe Deléham_, Aug 03 2012
%F A023607 a(n) = Sum_{i=1..n} A000045(i)*A000032(n-i+1). - _Vladimir Kruchinin_, Nov 08 2013
%p A023607 A023607 := proc(n)
%p A023607     n*combinat[fibonacci](n+1) ;
%p A023607 end proc:
%p A023607 seq(A023607(n),n=0..10) ; # _R. J. Mathar_, Jul 15 2017
%t A023607 Times@@@Thread[{Range[0, 50], Fibonacci[Range[51]]}]  (* _Harvey P. Dale_, Mar 08 2011 *)
%t A023607 Table[n*Fibonacci[n + 1], {n, 0, 50}]
%o A023607 (Haskell)
%o A023607 a023607 n = a023607_list !! n
%o A023607 a023607_list = zipWith (*) [0..] $ tail a000045_list
%o A023607 -- _Reinhard Zumkeller_, Oct 08 2012
%o A023607 (PARI) a(n)=n*fibonacci(n+1) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A023607 First differences of A094584.
%Y A023607 Second column of triangle A016095.
%Y A023607 Cf. A000045, A104796.
%K A023607 nonn,easy
%O A023607 0,3
%A A023607 _Clark Kimberling_
%E A023607 Simpler description from Samuel Lachterman (slachterman(AT)fuse.net), Sep 19 2003
%E A023607 Name improved by _T. D. Noe_, Mar 08 2011