A354302 a(n) is the numerator of Sum_{k=0..n} 1 / (k!)^2.

1, 2, 9, 41, 1313, 5471, 1181737, 28952557, 1235309099, 150090055529, 30018011105801, 201787741322329, 523033825507476769, 44196358255381786981, 5774990812036553498851, 1949059399062336805862213, 997918412319916444601453057, 3697415655903280160125896583

Offset

0,2

Links

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

Formula

Numerators of coefficients in expansion of BesselI(0,2*sqrt(x)) / (1 - x).

Example

1, 2, 9/4, 41/18, 1313/576, 5471/2400, 1181737/518400, 28952557/12700800, 1235309099/541900800, ...

Mathematica

Table[Sum[1/(k!)^2, {k, 0, n}], {n, 0, 17}] // Numerator
nmax = 17; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator

Crossrefs

Cf. A001044, A006040, A053557, A061354, A070910, A103816, A120265, A143382, A354303 (denominators), A354304.

Sequence in context: A020038 A330016 A056845 * A162273 A289684 A368764

Adjacent sequences: A354299 A354300 A354301 * A354303 A354304 A354305

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 23 2022

Status

approved