login
A028330
Elements to the right of the central elements of the even-Pascal triangle A028326.
7
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
0,1
LINKS
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)
EXAMPLE
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;
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 *)
PROG
(Magma)
[[2*Binomial(n, k): k in [Floor((n+2)/2)..n]]: n in [1..12]]; // 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
KEYWORD
nonn,tabf
EXTENSIONS
More terms from James A. Sellers
STATUS
approved