A354304 -id:A354304 - cp's OEIS frontend

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

Ilya Gutkovskiy, May 23 2022

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

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

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

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

A354305 a(n) is the denominator of Sum_{k=0..n} (-1)^k / (k!)^2.

Original entry on oeis.org

1, 1, 4, 9, 192, 1800, 103680, 529200, 232243200, 8230118400, 1463132160000, 39833773056000, 20858412072960000, 1615657835151360000, 584619573580922880000, 1908495817772544000000, 29184209113159670169600000, 3953548328298349068288000000, 185476873609942457647104000000

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, A053556, A061355, A073701, A091681, A143383, A354303, A354304 (numerators).

Table[Sum[(-1)^k/(k!)^2, {k, 0, n}], {n, 0, 18}] // Denominator
nmax = 18; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Denominator
Accumulate[Table[(-1)^k/(k!)^2,{k,0,20}]]//Denominator (* Harvey P. Dale, Apr 25 2023 *)

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

cp's OEIS Frontend

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

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