A138780 Triangle read by rows: T(n,k)=k*binomial(n-2k,3k+2) (n>=7, 1<=k<=(n-2)/5).

1, 6, 21, 56, 126, 252, 2, 462, 18, 792, 90, 1287, 330, 2002, 990, 3003, 2574, 3, 4368, 6006, 36, 6188, 12870, 234, 8568, 25740, 1092, 11628, 48620, 4095, 15504, 87516, 13104, 4, 20349, 151164, 37128, 60

Offset: 7

Author

Emeric Deutsch, May 10 2008

Keywords

• nonn
• tabf

Comments

Row n contains floor((n-2)/5) terms.

Row sums yield A137361.

References

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

Crossrefs

Cf. A137361.

Programs

Maple

T:=proc(n,k) options operator, arrow: k*binomial(n-2*k, 3*k+2) end proc: for n from 7 to 23 do seq(T(n,k),k=1..(n-2)*1/5) end do; # yields sequence in triangular form

Mathematica

Flatten[Table[k*Binomial[n-2k,3k+2],{n,7,30},{k,1,(n-2)/5}]] (* Harvey P. Dale, Aug 22 2015 *)