A138777 Triangle read by rows: T(n,k)=binomial(n-2k,3k+2) (n>=2, 0<=k<=(n-2)/5).

1, 3, 6, 10, 15, 21, 1, 28, 6, 36, 21, 45, 56, 55, 126, 66, 252, 1, 78, 462, 9, 91, 792, 45, 105, 1287, 165, 120, 2002, 495, 136, 3003, 1287, 1, 153, 4368, 3003, 12, 171, 6188, 6435, 78, 190, 8568, 12870, 364

Offset: 2

Author

Emeric Deutsch, May 10 2008

Keywords

• nonn
• tabf

Comments

Row n contains floor((n+3)/5) terms.

Row sums yield A137358.

References

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

Crossrefs

Cf. A137358.

Programs

Maple

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

Mathematica

Flatten[Table[Binomial[n-2k,3k+2],{n,2,20},{k,0,(n-2)/5}]] (* Harvey P. Dale, Mar 07 2013 *)