A336809 a(n) = (n!)^2 * Sum_{k=0..n} (k+1) / ((n-k)!)^2.

1, 3, 21, 271, 5649, 174051, 7447573, 422836191, 30767443521, 2792343036259, 309252314731701, 41051709426337743, 6434479982900111761, 1175819833620882461571, 247785659825802622964469, 59649892258930263778729951, 16268290830606063971956320513

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

Mathematica

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

Crossrefs

Cf. A001339, A006040.

Sequence in context: A277454 A215127 A227820 * A066206 A130032 A174967

Adjacent sequences: A336806 A336807 A336808 * A336810 A336811 A336812

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 27 2021

Status

approved