A354303 a(n) is the denominator of Sum_{k=0..n} 1 / (k!)^2.

1, 1, 4, 18, 576, 2400, 518400, 12700800, 541900800, 65840947200, 13168189440000, 88519495680000, 229442532802560000, 19387894021816320000, 2533351485517332480000, 855006126362099712000000, 437763136697395052544000000, 1621968544942912438272000000

Offset

0,3

Links

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

Formula

Denominators 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}] // Denominator
nmax = 17; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Denominator

Crossrefs

Cf. A001044, A006040, A053556, A061355, A070910, A143383, A354302 (numerators), A354305.

Sequence in context: A156522 A086400 A082022 * A114574 A295223 A173222

Adjacent sequences: A354300 A354301 A354302 * A354304 A354305 A354306

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 23 2022

Status

approved