A138778 Triangle read by rows: T(n,k)=k*binomial(n-2k,3k) (n>=5, 1<=k<=n/5).

1, 4, 10, 20, 35, 56, 2, 84, 14, 120, 56, 165, 168, 220, 420, 286, 924, 3, 364, 1848, 30, 455, 3432, 165, 560, 6006, 660, 680, 10010, 2145, 816, 16016, 6006, 4, 969, 24752, 15015, 52, 1140, 37128, 34320, 364

Offset: 5

Author

Emeric Deutsch, May 10 2008

Keywords

• nonn
• tabf

Comments

Row n contains floor(n/5) terms.

Row sums yield A137359.

References

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

Crossrefs

Cf. A137359.

Programs

Maple

T:=proc(n,k) options operator, arrow: k*binomial(n-2*k,3*k) end proc: for n from 5 to 22 do seq(T(n,k),k=1..(1/5)*n) end do; # yields sequence in triangular form

Mathematica

Flatten[Table[k*Binomial[n-2k,3k],{n,5,30},{k,1,n/5}]] (* Harvey P. Dale, Dec 20 2014 *)