# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a336608 Showing 1-1 of 1 %I A336608 #4 Jul 27 2020 15:48:38 %S A336608 1,0,1,4,51,856,21435,725796,32132499,1800176176,124511280723, %T A336608 10420458131260,1037868062069113,121317006426807192, %U A336608 16446390218708245393,2559445829942874207804,453188354421968867989395,90587738500599611033753184 %N A336608 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-x) / BesselJ(0,2*sqrt(x)). %F A336608 a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000275(k) / k!. %t A336608 nmax = 17; CoefficientList[Series[Exp[-x]/BesselJ[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2 %t A336608 A000275[0] = 1; A000275[n_] := A000275[n] = -Sum[(-1)^(n - k) Binomial[n, k]^2 A000275[k], {k, 0, n - 1}]; a[n_] := n! Sum[(-1)^(n - k) Binomial[n, k] A000275[k]/k!, {k, 0, n}]; Table[a[n], {n, 0, 17}] %Y A336608 Cf. A000275, A002720, A009940, A336606. %K A336608 nonn %O A336608 0,4 %A A336608 _Ilya Gutkovskiy_, Jul 27 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE