A340887 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * 3^(n-k-1) * a(k).

1, 1, 7, 99, 2511, 99531, 5680125, 441226521, 44766049599, 5748319130283, 911271895816077, 174799606363478361, 39903413238125862309, 10690643656077551475921, 3321750648705212259711063, 1184831658624977151885176859, 480843465699932167142334581919

Offset: 0

Author

Ilya Gutkovskiy, Jan 25 2021

Keywords

• nonn

Crossrefs

Cf. A102221, A255927, A340886, A340888.

Programs

Mathematica

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

Formula

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