A138779 Triangle read by rows: T(n,k)=k*binomial(n-2k,3k+1) (n>=6, 0<=k<=(n-1)/5).

1, 5, 15, 35, 70, 126, 2, 210, 16, 330, 72, 495, 240, 715, 660, 1001, 1584, 3, 1365, 3432, 33, 1820, 6864, 198, 2380, 12870, 858, 3060, 22880, 3003, 3876, 38896, 9009, 4, 4845, 63648, 24024, 56, 5985, 100776, 58344, 420

Offset: 6

Author

Emeric Deutsch, May 10 2008

Keywords

• nonn
• tabf

Comments

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

Row sums yield A137360.

References

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

Crossrefs

Cf. A137360.

Programs

Maple

T:=proc(n,k) options operator, arrow: k*binomial(n-2*k,3*k+1) end proc: for n from 6 to 23 do seq(T(n,k),k=1..(n-1)*1/5) end do; # yields sequence in triangular form

Mathematica

Select[Flatten[Table[k*Binomial[n-2k,3k+1],{n,6,30},{k,0,(n-1)/5}]], #>0&] (* Harvey P. Dale, May 24 2015 *)