A214590
Number of nXnXn triangular 0..3 arrays with every horizontal row having the same average value.
Original entry on oeis.org
4, 8, 62, 1862, 187862, 63120962, 71200442882, 272199293130242, 3552472974642762242, 159161446682919676638722, 24593308418551382594861736962, 13156534644821921838477614251069442
Offset: 1
Some solutions for n=4
.....2........2........2........2........2........1........2........2
....1.3......1.3......3.1......2.2......3.1......0.2......3.1......2.2
...1.3.2....3.2.1....2.3.1....3.0.3....0.3.3....1.0.2....2.3.1....3.0.3
..1.2.2.3..3.0.3.2..3.2.3.0..0.3.3.2..3.2.1.2..0.0.3.1..3.0.3.2..3.2.0.3
A386649
Product of first n central trinomial coefficients (A002426) for n > 0 with a(0) = 1.
Original entry on oeis.org
1, 1, 3, 21, 399, 20349, 2869209, 1127599137, 1248252244659, 3918263795984601, 35080215765450132753, 899912775031092255512709, 66403663756769266442027284401, 14140062564030204365431731967633341, 8713488333644640745496899895218790824407
Offset: 0
The central trinomial coefficients A002426(n) = [x^n] (1 + x + x^2)^n for n >= 0 begin [1, 1, 3, 7, 19, 51, 141, 393, 1107, 3139, ...], where a(n) equals the product of the terms A002426(0) through A002426(n).
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Table[Product[3^k * Hypergeometric2F1[1/2, -k, 1, 4/3], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 09 2025 *)
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{a(n) = prod(k=0,n, polcoef((1 + x + x^2)^k, k) )}
for(n=0,15,print1(a(n),", "))
Showing 1-2 of 2 results.
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