A337826 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k^4 * a(n-k).

1, 1, 10, 105, 2248, 62445, 2390436, 116650177, 7043659904, 514744959321, 44534754680500, 4493090921151261, 521600149636044480, 68900819660071184149, 10259571068808850618480, 1708054303772376318547125, 315688007001129064574027776, 64370788231256983836207599153

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

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

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

Mathematica

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}]
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

Crossrefs

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

Sequence in context: A193274 A068883 A087599 * A226360 A068097 A190956

Adjacent sequences: A337823 A337824 A337825 * A337827 A337828 A337829

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 24 2020

Status

approved