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 A056158 #37 Sep 16 2022 15:26:40
%S A056158 -4,-2,-4,2,-20,86,-532,3706,-29668,266990,-2669924,29369138,
%T A056158 -352429684,4581585862,-64142202100,962133031466,-15394128503492,
%U A056158 261700184559326,-4710603322067908,89501463119290210,-1790029262385804244
%N A056158 Equivalent of the Kurepa hypothesis for left factorial.
%C A056158 For a prime p > 2 we have !p == -a(p) mod p, where the left factorial !n = Sum_{k=0..n-1} k! (A003422).
%H A056158 James Spahlinger, <a href="/A056158/b056158.txt">Table of n, a(n) for n = 3..100</a>
%H A056158 Romeo Mestrovic, <a href="http://arxiv.org/abs/1312.7037">Variations of Kurepa's left factorial hypothesis</a>, arXiv:1312.7037 [math.NT], 2013.
%H A056158 Romeo Mestrovic, <a href="https://doi.org/10.2298/FIL1510207M">The Kurepa-Vandermonde matrices arising from Kurepa's left factorial hypothesis</a>, Filomat 29:10 (2015), 2207-2215; DOI 10.2298/FIL1510207M.
%F A056158 a(3) = -4, a(n) = -(n-3)*a(n-1) - 2*(n-1).
%F A056158 a(n) = 2*(-1)^(n-1)*(n-3)!*Sum_{k=0..n-3} frac((k+2)*(-1)^(k+1))*k!.
%F A056158 Conjecture: a(n) + (n-5)*a(n-1) + (-2*n+9)*a(n-2) + (n-5)*a(n-3) = 0. - _R. J. Mathar_, Jan 31 2014
%F A056158 a(n) ~ (-1)^n * 2 * exp(-1) * (n-3)!. - _Vaclav Kotesovec_, Jan 05 2019
%F A056158 G.f.: 2*x^2*(exp(-1+1/x) * Exponential-Integral((x-1)/x) + x/(x-1)). - _G. C. Greubel_, Mar 29 2019
%t A056158 a[3] = -4; a[n_]:= -(n-3)*a[n-1] - 2*(n-1); Array[a, 30, 3] (* _James Spahlinger_, Feb 20 2016 *)
%t A056158 Drop[CoefficientList[Series[2*x^2*(Exp[1/x -1]*ExpIntegralEi[(x-1)/x] + x/(x-1)), {x,0,15}, Assumptions -> x > 0], x],3] (* _G. C. Greubel_, Mar 29 2019 *)
%o A056158 (Magma) [n eq 3 select -4 else -(n-3)*Self(n-3)-2*(n-1): n in [3..30]]; // _Vincenzo Librandi_, Feb 22 2016
%o A056158 (PARI) m=30; v=concat([-4], vector(m-1)); for(n=2, m, v[n]=-(n-1)*v[n-1] -2*(n+1)); v \\ _G. C. Greubel_, Mar 29 2019
%o A056158 (Sage)
%o A056158 @CachedFunction
%o A056158 def Self(n):
%o A056158 if n == 3 : return -4
%o A056158 return -(n-3)*Self(n-1) - 2*(n-1)
%o A056158 [Self(n) for n in (3..30)] # _G. C. Greubel_, Mar 29 2019
%K A056158 sign,easy
%O A056158 3,1
%A A056158 _Aleksandar Petojevic_, Jul 31 2000
%E A056158 More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000