This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A028330 #17 Jul 02 2025 16:01:56
%S A028330 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,
%T A028330 420,240,90,20,2,924,660,330,110,22,2,1584,990,440,132,24,2,3432,2574,
%U A028330 1430,572,156,26,2,6006,4004,2002,728,182,28,2,12870,10010,6006,2730
%N A028330 Elements to the right of the central elements of the even-Pascal triangle A028326.
%H A028330 G. C. Greubel, <a href="/A028330/b028330.txt">Table of n, a(n) for n = 0..2549</a>
%F A028330 a(n) = 2 * A014413(n). - _Sean A. Irvine_, Dec 29 2019
%F A028330 From _G. C. Greubel_, Jul 14 2024: (Start)
%F A028330 T(n, k) = 2*binomial(n+1, k+1 + floor((n+1)/2)) for n >= 0, 0 <= k <= floor(n/2).
%F A028330 Sum_{k=0..floor(n/2)} T(n, k) = A202736(n+1) = 2*A058622(n+1).
%F A028330 Sum_{k=0..floor(n/2)} (-1)^k*T(n, k) = 2*A001405(n) = A063886(n+1). (End)
%e A028330 This sequence represents the following portion of A028330(n,k), with x being the elements of A028329(n):
%e A028330 x;
%e A028330 ., 2;
%e A028330 ., x, 2;
%e A028330 ., ., 6, 2;
%e A028330 ., ., x, 8, 2;
%e A028330 ., ., ., 20, 10, 2;
%e A028330 ., ., ., x, 30, 12, 2;
%e A028330 ., ., ., ., 70, 42, 14, 2;
%e A028330 ., ., ., ., x, 112, 56, 16, 2;
%e A028330 ., ., ., ., ., 252, 168, 72, 18, 2;
%e A028330 ., ., ., ., ., x, 420, 240, 90, 20, 2;
%e A028330 ., ., ., ., ., ., 924, 660, 330, 110, 22, 2;
%e A028330 ., ., ., ., ., ., x, 1584, 990, 440, 132, 24, 2;
%e A028330 As an irregular triangle:
%e A028330 2;
%e A028330 2;
%e A028330 6, 2;
%e A028330 8, 2;
%e A028330 20, 10, 2;
%e A028330 30, 12, 2;
%e A028330 70, 42, 14, 2;
%e A028330 112, 56, 16, 2;
%e A028330 252, 168, 72, 18, 2;
%e A028330 420, 240, 90, 20, 2;
%e A028330 924, 660, 330, 110, 22, 2;
%t A028330 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 *)
%o A028330 (Magma)
%o A028330 [[2*Binomial(n,k): k in [Floor((n+2)/2)..n]]: n in [1..12]]; // _G. C. Greubel_, Jul 14 2024
%o A028330 (SageMath)
%o A028330 def A028326(n,k): return 2*binomial(n, k)
%o A028330 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
%Y A028330 Cf. A028326, A028327, A028328, A028329, A028331, A028332.
%Y A028330 Cf. A001405, A014413, A058622, A063886, A202736.
%K A028330 nonn,tabf
%O A028330 0,1
%A A028330 _Mohammad K. Azarian_
%E A028330 More terms from _James Sellers_