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 A385286 #19 Jun 24 2025 16:15:18
%S A385286 1,8,120,2528,66424,2039808,70283424,2643158400,106391894904,
%T A385286 4518833256512,200396211454720,9205443151733760,435368682010660000,
%U A385286 21100379936684418560,1044115187294444772480,52597451834668445910528,2691037806733052553149304,139567074682665782246950080
%N A385286 a(n) = (n!)^2 [x^n] hypergeom([], [1], x)^8.
%C A385286 We regard this sequence in the list of sequences n -> A287316(n, 2^k) for k = 3.
%H A385286 Nikolai Beluhov, <a href="https://arxiv.org/abs/2506.12789">Powers of 2 in High-Dimensional Lattice Walks</a>, arXiv:2506.12789 [math.CO], 2025. See p. 19.
%F A385286 a(n) = (n!)^2 [x^n] BesselI(0, 2*sqrt(x))^8.
%F A385286 a(n) = A287316(n, 2^3).
%F A385286 a(n) ~ 2^(6*n+5) / (Pi^(7/2) * n^(7/2)). - _Vaclav Kotesovec_, Jun 24 2025
%p A385286 A385286_list := proc(len) local n; series(hypergeom([], [1], x)^8, x, len);
%p A385286 seq((n!)^2*coeff(%, x, n), n = 0..len-1) end: A385286_list(18);
%t A385286 nmax = 20; CoefficientList[Series[BesselI[0, 2*Sqrt[x]]^8, {x, 0, nmax}], x] * Range[0, nmax]!^2 (* _Vaclav Kotesovec_, Jun 24 2025 *)
%o A385286 (PARI) a(n) = my(x='x+O('x^(n+1))); n!^2*polcoeff(hypergeom([], [1], x)^8, n); \\ _Michel Marcus_, Jun 24 2025
%Y A385286 Cf. A000012 (k=0), A000984 (k=1), A002895 (k=2), this sequence (k=3), A287316.
%K A385286 nonn,walk
%O A385286 0,2
%A A385286 _Peter Luschny_, Jun 24 2025