A214589
Number of nXnXn triangular 0..2 arrays with every horizontal row having the same average value.
Original entry on oeis.org
3, 5, 23, 401, 20351, 2869211, 1127599139, 1248252244661, 3918263795984603, 35080215765450132755, 899912775031092255512711, 66403663756769266442027284403, 14140062564030204365431731967633343
Offset: 1
Some solutions for n=4
.....1........1........1........1........1........1........1........1
....1.1......2.0......0.2......0.2......0.2......2.0......0.2......1.1
...2.0.1....2.0.1....1.2.0....2.1.0....1.1.1....2.1.0....1.2.0....0.2.1
..0.2.1.1..1.0.1.2..0.2.2.0..1.2.0.1..2.1.1.0..0.1.1.2..0.2.1.1..0.0.2.2
A386650
Product of first n quadrinomial coefficients (A005725) for n > 0 with a(0) = 1.
Original entry on oeis.org
1, 1, 3, 30, 930, 93930, 31560480, 35600221440, 136099646565120, 1776236487321381120, 79580723341459838319360, 12296654209275691297430868480, 6578267322410960919238807125534720, 12223446894741861497849104893155093176320, 79112201841847644246811045518121813092796661760
Offset: 0
The quadrinomial coefficients A005725(n) = [x^n] (1 + x + x^2 + x^3)^n for n >= 0 begin [1, 1, 3, 10, 31, 101, 336, 1128, 3823, ...], where a(n) equals the product of the terms A005725(0) through A005725(n).
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Table[Product[HypergeometricPFQ[{(1-k)/2, -k, -k/2}, {1/2, 1}, -1], {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 + x^3)^k, k) )}
for(n=0, 15, print1(a(n), ", "))
Showing 1-2 of 2 results.
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