A354303 - OEIS

%I #6 May 24 2022 02:39:07

%S 1,1,4,18,576,2400,518400,12700800,541900800,65840947200,

%T 13168189440000,88519495680000,229442532802560000,

%U 19387894021816320000,2533351485517332480000,855006126362099712000000,437763136697395052544000000,1621968544942912438272000000

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

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

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

%t Table[Sum[1/(k!)^2, {k, 0, n}], {n, 0, 17}] // Denominator

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

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

%K nonn,frac

%O 0,3

%A _Ilya Gutkovskiy_, May 23 2022