A337591 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k^3 * a(n-k).

1, 1, 6, 51, 760, 15545, 428256, 15043483, 653049664, 34204348305, 2118834917200, 152834879685851, 12670536337934256, 1194143629239156505, 126753440317516749660, 15031687739886065433375, 1977667235694725269563136, 286890421090357737699794209, 45637300134026406622214264592

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

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

Mathematica

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[x BesselI[0, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A033462, A336227.

Sequence in context: A210810 A134276 A372333 * A125803 A197073 A271680

Adjacent sequences: A337588 A337589 A337590 * A337592 A337593 A337594

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 02 2020

Status

approved