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 A382848 #11 Jun 08 2025 03:33:37
%S A382848 1,1,-5,-35,-29,751,3991,-4115,-137885,-495269,2114245,25786795,
%T A382848 50109775,-627370925,-4643568305,-495798035,157753390435,768269873875,
%U A382848 -1851203127335,-35924154988865,-107001450483779,763444753890721,7510024190977105,8899910747771995
%N A382848 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k)^2 * binomial(n+k,k).
%C A382848 Diagonal of the rational function 1 / (1 + x + x*y + y*z + x*z + x*y*z).
%F A382848 (59*n-94)*n^2*a(n) = 5*(59*n^3-153*n^2+117*n-30)*a(n-1) - (2301*n^3-8268*n^2+9257*n-3050)*a(n-2) - 2*(59*n-35)*(n-2)^2*a(n-3) with a(0) = 1, a(1) = 1 and a(2) = -5. - _Peter Bala_, May 24 2025
%t A382848 Table[Sum[(-1)^(n - k) Binomial[n, k]^2 Binomial[n + k, k], {k, 0, n}], {n, 0, 23}]
%t A382848 Table[(-1)^n HypergeometricPFQ[{-n, -n, n + 1}, {1, 1}, -1], {n, 0, 23}]
%t A382848 Table[SeriesCoefficient[1/(1 + x + x y + y z + x z + x y z), {x, 0, n}, {y, 0, n}, {z, 0, n}], {n, 0, 23}]
%Y A382848 Cf. A005258, A026641, A126869, A245086, A382405, A382849.
%K A382848 sign
%O A382848 0,3
%A A382848 _Ilya Gutkovskiy_, Apr 06 2025