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

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

Offset: 0

Author

Ilya Gutkovskiy, May 23 2022

Keywords

• nonn
• frac

Examples

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

Crossrefs

Cf. A001044, A053556, A061355, A073701, A091681, A143383, A354303, A354304 (numerators).

Programs

Mathematica

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 *)

Formula

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