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A336809 a(n) = (n!)^2 * Sum_{k=0..n} (k+1) / ((n-k)!)^2. 1
1, 3, 21, 271, 5649, 174051, 7447573, 422836191, 30767443521, 2792343036259, 309252314731701, 41051709426337743, 6434479982900111761, 1175819833620882461571, 247785659825802622964469, 59649892258930263778729951, 16268290830606063971956320513 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 21:49 EST 2023. Contains 359849 sequences. (Running on oeis4.)