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a(n) = (1^n + 2^n +3^n + 4^n)/2.
2

%I #15 Oct 24 2024 02:20:32

%S 2,5,15,50,177,650,2445,9350,36177,141170,554325,2186750,8656377,

%T 34355690,136617405,544061750,2169039777,8654570210,34553579685,

%U 138020346350,551499730377,2204254480730,8811785649165,35231447872550,140878711512177,563373614503250

%N a(n) = (1^n + 2^n +3^n + 4^n)/2.

%C 2*a(n) = A001551(n), n>=0.

%F a(n) = (1^n + 2^n + 3^n + 4^n)/2, n>=0.

%F E.g.f.: (1-exp(4*x))/(2*(exp(-x)-1)) = Sum_{j=1..4} exp(j*x)/2.

%F O.g.f.: (2-5*x)*(1-5*x+5*x^2)/(Product_{j=1..4} (1-j*x)) (via Laplace transformation of the o.g.f.).

%t Table[Total[Range[4]^n]/2, {n, 0, 40}] (* _T. D. Noe_, Oct 10 2011 *)

%Y Cf. A001551/2.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Oct 10 2011