A120478 a(n) = binomial(n+6,5) - binomial(n,5).
6, 21, 56, 126, 252, 461, 786, 1266, 1946, 2877, 4116, 5726, 7776, 10341, 13502, 17346, 21966, 27461, 33936, 41502, 50276, 60381, 71946, 85106, 100002, 116781, 135596, 156606, 179976, 205877, 234486, 265986, 300566, 338421, 379752, 424766
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Maple
[seq(binomial(n+6,5)-binomial(n,5),n=0..45)];
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Mathematica
Table[Binomial[n+6,5]-Binomial[n,5],{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{6,21,56,126,252},40] (* Harvey P. Dale, May 04 2011 *)
Formula
a(n) = A008488(n+1). - R. J. Mathar, Aug 07 2008
From Harvey P. Dale, May 04 2011: (Start)
a(0)=6, a(1)=21, a(2)=56, a(3)=126, a(4)=252, a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
G.f.: (-6 + 9*x - 11*x^2 + 4*x^3 - 2*x^4)/(-1 + x)^5. (End)