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 A382842 #11 Apr 09 2025 05:05:52
%S A382842 1,1,9,217,1945,35001,764001,12079089,250222617,5424133465,
%T A382842 107360983009,2358751625649,52540471866961,1147794435985393,
%U A382842 26151265459123065,600227875293254217,13779170435209475097,322302377797126709913,7582484532013652243169,179184911648568670363185,4275721755296040840336945
%N A382842 a(n) = Sum_{k=0..floor(n/2)} (binomial(n,k) * binomial(n-k,k))^3.
%C A382842 Diagonal of the rational function 1 / ((1 - x)*(1 - y)*(1 - z)*(1 - u)*(1 - v)*(1 - w) - (x*y*z)^2*u*v*w).
%F A382842 a(n) ~ 3^(3*n+3) / (8 * Pi^(5/2) * n^(5/2)). - _Vaclav Kotesovec_, Apr 07 2025
%F A382842 a(n) = Sum_{k=0..floor(n/2)} A089627(n,k)^3. - _Alois P. Heinz_, Apr 07 2025
%p A382842 a:= n-> add(combinat[multinomial](n, n-2*k, k$2)^3, k=0..n/2):
%p A382842 seq(a(n), n=0..20); # _Alois P. Heinz_, Apr 07 2025
%t A382842 Table[Sum[(Binomial[n, k] Binomial[n - k, k])^3, {k, 0, Floor[n/2]}], {n, 0, 20}]
%t A382842 Table[HypergeometricPFQ[{1/2 - n/2, 1/2 - n/2, 1/2 - n/2, -n/2, -n/2, -n/2}, {1, 1, 1, 1, 1}, 64], {n, 0, 20}]
%t A382842 Table[SeriesCoefficient[1/((1 - x) (1 - y) (1 - z) (1 - u) (1 - v) (1 - w) - (x y z)^2 u v w), {x, 0, n}, {y, 0, n}, {z, 0, n}, {u, 0, n}, {v, 0, n}, {w, 0, n}], {n, 0, 20}]
%Y A382842 Cf. A000172, A002426, A069865, A092813, A181545, A382841.
%Y A382842 Cf. A089627.
%K A382842 nonn
%O A382842 0,3
%A A382842 _Ilya Gutkovskiy_, Apr 06 2025