A138776 Triangle read by rows: T(n,k)=binomial(n-2k,3k+1) (n>=1, 0<=k<=(n-1)/5).

1, 2, 3, 4, 5, 6, 1, 7, 5, 8, 15, 9, 35, 10, 70, 11, 126, 1, 12, 210, 8, 13, 330, 36, 14, 495, 120, 15, 715, 330, 16, 1001, 792, 1, 17, 1365, 1716, 11, 18, 1820, 3432, 66, 19, 2380, 6435, 286, 20, 3060, 11440, 1001

Offset: 1

Author

Emeric Deutsch, May 10 2008

Keywords

• nonn
• tabf

Comments

Row n contains floor((n+4)/5) terms.

Row sums yield A137357.

References

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

Crossrefs

Cf. A137357.

Programs

Maple

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

Mathematica

Table[Binomial[n-2k,3k+1],{n,30},{k,0,(n-1)/5}]//Flatten (* Harvey P. Dale, Aug 12 2018 *)