A138775 Triangle read by rows: T(n,k)=binomial(n-2k,3k) (n>=0, 0<=k<=n/5).

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 10, 1, 20, 1, 35, 1, 56, 1, 1, 84, 7, 1, 120, 28, 1, 165, 84, 1, 220, 210, 1, 286, 462, 1, 1, 364, 924, 10, 1, 455, 1716, 55, 1, 560, 3003, 220, 1, 680, 5005, 715, 1, 816, 8008, 2002, 1

Offset: 0

Author

Emeric Deutsch, May 10 2008

Keywords

• nonn
• tabf

Comments

Row n contains 1+floor(n/5) terms.

Row sums yield A137356.

References

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

Crossrefs

Cf. A137356.

Programs

Maple

T:=proc(n,k) options operator, arrow: binomial(n-2*k, 3*k) end proc: for n from 0 to 20 do seq(T(n,k),k=0..(1/5)*n) end do; # yields sequence in triangular form

Mathematica

Flatten[Table[Binomial[n-2k,3k],{n,0,20},{k,0,Floor[n/5]}]] (* Harvey P. Dale, Oct 14 2012 *)