A354305 - OEIS

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

EXAMPLE

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

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