A103437 Sum_{i>=1} (i^n*Lucas(i)/2^i).

4, 22, 210, 2974, 56130, 1324222, 37489410, 1238235454, 46740118530, 1984855550782, 93653819396610, 4860878501987134, 275227990564092930, 16882335978752910142, 1115211301788480951810, 78930528072274523870014

Offset: 0

Author

Ralf Stephan, Feb 08 2005

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..356

Crossrefs

Cf. A000032.

Programs

Maple

V:=2*exp(x)*(exp(x)+1)/(4-2*exp(x)-exp(2*x)):
S:= series(V,x,51):
seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Jan 24 2017

Formula

From Robert Israel, Jan 24 2017: (Start)

a(n) = polylog(-n, (sqrt(5)+1)/4) + polylog(-n, (-sqrt(5)+1)/4).

E.g.f.: 2*exp(x)*(exp(x)+1)/(4-2*exp(x)-exp(2*x)). (End)

a(n) ~ n! / (log(sqrt(5)-1))^(n+1). - Vaclav Kotesovec, Jan 24 2017