A137361 a(n) = Sum_{k=0..n/2} k*binomial(n-2*k, 3*k+2).

0, 0, 0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 254, 480, 882, 1617, 2992, 5580, 10410, 19292, 35400, 64343, 116128, 208701, 374226, 670095, 1198164, 2138423, 3808148, 6766089, 11996042, 21229790, 37513896, 66202347, 116692472, 205458357, 361349662, 634845141, 1114205988

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

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A137356-A137360, A136444.

Programs

Magma

[&+[k*Binomial(n-2*k, 3*k+2): k in [0..(n div 2)]]: n in [0..40]]; // Bruno Berselli, Feb 13 2015

Maple

a:= n-> (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)[1,8]:
seq(a(n), n=0..50);  # Alois P. Heinz, Oct 23 2008

Mathematica

t[i_, j_] := If[i == j-1, 1, If[j == 1, {6, -15, 20, -15, 8, -7, 6, -2, 0, -1}[[i]] , 0]]; M = Array[t, {10, 10}]; a[n_] := MatrixPower[M, n][[1, 8]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 13 2015, after Alois P. Heinz *)

Formula

G.f.: x^7/(x^5 + x^3 - 3*x^2 + 3*x - 1)^2. - Alois P. Heinz, Oct 23 2008