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A103437
Sum_{i>=1} (i^n*Lucas(i)/2^i).
2
4, 22, 210, 2974, 56130, 1324222, 37489410, 1238235454, 46740118530, 1984855550782, 93653819396610, 4860878501987134, 275227990564092930, 16882335978752910142, 1115211301788480951810, 78930528072274523870014
OFFSET
0,1
LINKS
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
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
CROSSREFS
Cf. A000032.
Sequence in context: A183274 A303330 A280828 * A215201 A063380 A113385
KEYWORD
nonn
AUTHOR
Ralf Stephan, Feb 08 2005
STATUS
approved