A034850 Triangular array formed by taking every other term of Pascal's triangle.

1, 1, 2, 1, 3, 1, 6, 1, 5, 10, 1, 6, 20, 6, 1, 21, 35, 7, 1, 28, 70, 28, 1, 9, 84, 126, 36, 1, 10, 120, 252, 120, 10, 1, 55, 330, 462, 165, 11, 1, 66, 495, 924, 495, 66, 1, 13, 286, 1287, 1716, 715, 78, 1, 14, 364, 2002, 3432, 2002, 364, 14, 1, 105, 1365, 5005, 6435

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• tabf

Examples

			Triangle begins:
  1;
  1;
  2;
  1,  3;
  1,  6,  1;
  5, 10,  1;
  6, 20,  6;
  1, 21, 35,  7;
		

Links

• G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
• D. Dumont and J. Zeng, Polynômes d'Euler et les fractions continues de Stieltjes-Rogers, preprint 1996.
• D. Dumont and J. Zeng, Polynômes d'Euler et les fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998) 3, 387-410.

Crossrefs

Cf. A007318, A034839.

Programs

Mathematica

Table[If[k < 0 || k > (Floor[n/4] + Floor[(n + 1)/4]), 0, Binomial[n, 2*k + Mod[Floor[(n + 1)/2], 2]]], {n, 0, 20}, {k, 0, (Floor[n/4] + Floor[(n + 1)/4])}] // Flatten (* G. C. Greubel, Feb 23 2018 *)

PARI

{T(n, k) = if( k<0 || k>n\4 + (n+1)\4, 0, binomial(n, 2*k + (n+1)\2%2))}; /* Michael Somos, Feb 11 2004 */

Formula

a(n) = A007318(2n) if both are regarded as integer sequences. - Michael Somos, Feb 11 2004