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 A096789 #35 Apr 08 2025 23:17:58
%S A096789 1,5,9,0,6,3,6,8,5,4,6,3,7,3,2,9,0,6,3,3,8,2,2,5,4,4,2,4,9,9,9,6,6,6,
%T A096789 2,4,7,9,5,4,4,7,8,1,5,9,4,9,5,5,3,6,6,4,7,1,3,2,2,8,7,9,8,4,6,0,8,5,
%U A096789 4,5,0,3,7,5,3,5,3,6,1,1,8,5,1,1,6,1,2,2,1,4,7,5,9,4,2,2,8,9,2,5,2,3,7,7,5
%N A096789 Decimal expansion of BesselI(1,2).
%H A096789 A.H.M. Smeets, <a href="/A096789/b096789.txt">Table of n, a(n) for n = 1..20000</a>
%H A096789 I. S. Gradsteyn and I. M. Ryzhik, <a href="http://mathtable.com/gr/index.html">Table of integrals, series and products</a> (6th ed.), 2000, (eq. 0.246.2).
%H A096789 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html">Modified Bessel Function of the First Kind</a>.
%F A096789 Equals Sum_{k >= 0} k/k!^2.
%F A096789 Continued fraction expansion: 1/(1 - 1/(3 - 2/(7 - 6/(13 - 12/(21 - ... - n*(n-1)/(n^2+n+1 - ...)))))). For a sketch of the proof see A228229. Cf. A070910. - _Peter Bala_, Aug 19 2013
%F A096789 From _Amiram Eldar_, Jul 09 2023: (Start)
%F A096789 Equals exp(-2) * Sum_{k>=1} A000108(k)/(k-1)!.
%F A096789 Equals exp(2) * Sum_{k>=1} (-1)^(k+1) * A000108(k)/(k-1)!. (End)
%e A096789 1.59063685463732906338225...
%p A096789 evalf(BesselI(1,2)). # _R. J. Mathar_, Oct 16 2015
%t A096789 RealDigits[BesselI[1, 2], 10, 110][[1]]
%t A096789 (* Or *) RealDigits[ Sum[ n/(n!n!), {n, 0, Infinity}], 10, 110][[1]]
%o A096789 (PARI) besseli(1,2) \\ _Charles R Greathouse IV_, Feb 19 2014
%Y A096789 Cf. A000108, A070910, A228229, A348607.
%K A096789 cons,easy,nonn
%O A096789 1,2
%A A096789 _Robert G. Wilson v_, Jul 09 2004