A335946 a(n) = 1 + Sum_{k=0..n-1} binomial(n,k)^2 * a(k).

1, 2, 10, 110, 2154, 65902, 2903446, 174109546, 13636888810, 1351801926542, 165434393561910, 24497621303302666, 4317170011370444982, 892891315599103615082, 214174328063904077240962, 58974283594413521123672110, 18476316023495768160707616490

Offset: 0

Author

Ilya Gutkovskiy, Jul 01 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..248

Crossrefs

Row sums of A102220.

Cf. A000629, A102221.

Programs

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n, k]^2 a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(2 - BesselI[0, 2 Sqrt[x]]), {x, 0, nmax}], x] Range[0, nmax]!^2

Formula

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

a(n) = 2 * A102221(n) for n > 0.