A137360 a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k+1).

0, 0, 0, 0, 0, 0, 1, 5, 15, 35, 70, 128, 226, 402, 735, 1375, 2588, 4830, 8882, 16108, 28943, 51785, 92573, 165525, 295869, 528069, 940259, 1669725, 2957941, 5229953, 9233748, 16284106, 28688451, 50490125, 88765885, 155891305, 273495479, 479360847, 839451764

Offset: 0

Author

Don Knuth, Apr 11 2008

Keywords

• nonn

References

• D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 8, -7, 6, -2, 0, -1).

Crossrefs

Cf. A137356-A137361, A136444.

Programs

Maple

a:= n-> (Matrix([[35, 15, 5, 1, 0$6]]). Matrix (10, (i,j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1,10]: seq (a(n), n=0..50);  # Alois P. Heinz, Oct 23 2008

Mathematica

Table[Sum[k Binomial[n-2k,3k+1],{k,n/2}],{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,8,-7,6,-2,0,-1},{0,0,0,0,0,0,1,5,15,35},40] (* Harvey P. Dale, May 31 2017 *)

Formula

G.f.: x^6*(1-x)/(x^5+x^3-3*x^2+3*x-1)^2. - Alois P. Heinz, Oct 23 2008