A340887 - OEIS

%I #5 Jan 25 2021 19:04:54

%S 1,1,7,99,2511,99531,5680125,441226521,44766049599,5748319130283,

%T 911271895816077,174799606363478361,39903413238125862309,

%U 10690643656077551475921,3321750648705212259711063,1184831658624977151885176859,480843465699932167142334581919

%N a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 3^(n-k-1) * a(k).

%F Sum_{n>=0} a(n) * x^n / (n!)^2 = 3 / (4 - BesselI(0,2*sqrt(3*x))).

%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]^2 3^(n - k - 1) a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

%t nmax = 16; CoefficientList[Series[3/(4 - BesselI[0, 2 Sqrt[3 x]]), {x, 0, nmax}], x] Range[0, nmax]!^2

%Y Cf. A102221, A255927, A340886, A340888.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 25 2021