A196836 a(n) = (1^n + 2^n +3^n + 4^n)/2.

2, 5, 15, 50, 177, 650, 2445, 9350, 36177, 141170, 554325, 2186750, 8656377, 34355690, 136617405, 544061750, 2169039777, 8654570210, 34553579685, 138020346350, 551499730377, 2204254480730, 8811785649165, 35231447872550, 140878711512177, 563373614503250

Offset: 0

Author

Wolfdieter Lang, Oct 10 2011

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A001551/2.

Programs

Mathematica

Table[Total[Range[4]^n]/2, {n, 0, 40}] (* T. D. Noe, Oct 10 2011 *)

Formula

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

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

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.).