%I #4 Sep 24 2020 14:00:08

%S 1,1,10,105,2248,62445,2390436,116650177,7043659904,514744959321,

%T 44534754680500,4493090921151261,521600149636044480,

%U 68900819660071184149,10259571068808850618480,1708054303772376318547125,315688007001129064574027776,64370788231256983836207599153

%N a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k^4 * a(n-k).

%F Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x * (BesselI(0,2*sqrt(x)) + sqrt(x) * BesselI(1,2*sqrt(x)))).

%F Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(Sum_{n>=1} n^3 * x^n / (n!)^2).

%t a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k^4 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]

%t nmax = 17; CoefficientList[Series[Exp[x (BesselI[0, 2 Sqrt[x]] + Sqrt[x] BesselI[1, 2 Sqrt[x]])], {x, 0, nmax}], x] Range[0, nmax]!^2

%Y Cf. A023998, A279358, A336227, A337591, A337825.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 24 2020