A103436 a(n) = Sum_{i>=1} i^n*Fibonacci(i)/2^i.

2, 10, 94, 1330, 25102, 592210, 16765774, 553755730, 20902816462, 887654387410, 41883261304654, 2173850952162130, 123085699242396622, 7550010173496390610, 498737656015015238734, 35298805253912253800530

Offset

0,1

References

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 141.

Links

Amiram Eldar, Table of n, a(n) for n = 0..357

Arthur T. Benjamin, Judson D. Neer, Daniel T. Otero and James A. Sellers, A probabilistic view of certain weighted Fibonacci sums, Fibonacci Quarterly, Vol. 41, No. 4 (2002), pp. 360-364.

Formula

a(n) = (PolyLog(-n, (1 + sqrt(5))/4) - PolyLog(-n, (1 - sqrt(5))/4))/sqrt(5). - Vladimir Reshetnikov, Jan 20 2011

a(n) = 2 * A098799(n). - Amiram Eldar, Jun 16 2020

Mathematica

a[n_] := Simplify[(PolyLog[-n, GoldenRatio/2] - PolyLog [-n, (1-GoldenRatio)/2]) / Sqrt[5]]; Array[a, 20, 0] (* Amiram Eldar, Jun 16 2020 *)

Crossrefs

Cf. A000045, A098799.

Sequence in context: A231375 A100622 A355782 * A182173 A362643 A160940

Adjacent sequences: A103433 A103434 A103435 * A103437 A103438 A103439

Keyword

nonn

Author

Ralf Stephan, Feb 08 2005

Status

approved