A354302 -id:A354302 - cp's OEIS frontend

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

Ilya Gutkovskiy, May 23 2022

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

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

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

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

A354304 a(n) is the numerator of Sum_{k=0..n} (-1)^k / (k!)^2.

Original entry on oeis.org

1, 0, 1, 2, 43, 403, 23213, 118483, 51997111, 1842647621, 327581799289, 8918414485643, 4670006130663971, 361730891537680087, 130890931830249779173, 427294615628884602769, 6534075316966068976316143, 885163015595247156635327497, 41526561745210509140249210357

Offset: 0

Ilya Gutkovskiy, May 23 2022

			1, 0, 1/4, 2/9, 43/192, 403/1800, 23213/103680, 118483/529200, 51997111/232243200, 1842647621/8230118400, ...

Cf. A001044, A053557, A061354, A073701, A091681, A103816, A120265, A143382, A354302, A354305 (denominators).

Table[Sum[(-1)^k/(k!)^2, {k, 0, n}], {n, 0, 18}] // Numerator
nmax = 18; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator

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

cp's OEIS Frontend

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

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