A028330 Elements to the right of the central elements of the even-Pascal triangle A028326.

2, 2, 6, 2, 8, 2, 20, 10, 2, 30, 12, 2, 70, 42, 14, 2, 112, 56, 16, 2, 252, 168, 72, 18, 2, 420, 240, 90, 20, 2, 924, 660, 330, 110, 22, 2, 1584, 990, 440, 132, 24, 2, 3432, 2574, 1430, 572, 156, 26, 2, 6006, 4004, 2002, 728, 182, 28, 2, 12870, 10010, 6006, 2730

Offset: 0

Author

Mohammad K. Azarian

Keywords

• nonn
• tabf

Examples

			This sequence represents the following portion of A028330(n,k), with x being the elements of A028329(n):
  x;
  .,  2;
  .,  x,  2;
  .,  .,  6,  2;
  .,  .,  x,  8,  2;
  .,  .,  ., 20, 10,   2;
  .,  .,  .,  x, 30,  12,   2;
  .,  .,  .,  ., 70,  42,  14,    2;
  .,  .,  .,  .,  x, 112,  56,   16,   2;
  .,  .,  .,  .,  ., 252, 168,   72,  18,   2;
  .,  .,  .,  .,  .,   x, 420,  240,  90,  20,   2;
  .,  .,  .,  .,  .,   ., 924,  660, 330, 110,  22,  2;
  .,  .,  .,  .,  .,   .,   x, 1584, 990, 440, 132, 24, 2;
As an irregular triangle:
    2;
    2;
    6,   2;
    8,   2;
   20,  10,   2;
   30,  12,   2;
   70,  42,  14,   2;
  112,  56,  16,   2;
  252, 168,  72,  18,  2;
  420, 240,  90,  20,  2;
  924, 660, 330, 110, 22,  2;
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2549

Crossrefs

Cf. A028326, A028327, A028328, A028329, A028331, A028332.

Cf. A001405, A014413, A058622, A063886, A202736.

Programs

Magma

[[2*Binomial(n,k): k in [Floor((n+2)/2)..n]]: n in [1..12]]; // G. C. Greubel, Jul 14 2024

Mathematica

Table[2*Binomial[n+1, k+1 +Floor[(n+1)/2]], {n,0,12}, {k,0,Floor[n/2] }]//Flatten (* G. C. Greubel, Jul 14 2024 *)

SageMath

def A028326(n,k): return 2*binomial(n, k)
flatten([[A028326(n,k) for k in range(((n+2)//2), n+1)] for n in range(1,21)]) # G. C. Greubel, Jul 14 2024

Formula

a(n) = 2 * A014413(n). - Sean A. Irvine, Dec 29 2019

From G. C. Greubel, Jul 14 2024: (Start)

T(n, k) = 2*binomial(n+1, k+1 + floor((n+1)/2)) for n >= 0, 0 <= k <= floor(n/2).

Sum_{k=0..floor(n/2)} T(n, k) = A202736(n+1) = 2*A058622(n+1).

Sum_{k=0..floor(n/2)} (-1)^k*T(n, k) = 2*A001405(n) = A063886(n+1). (End)

Extensions

More terms from James Sellers