A354302 - OEIS

%I #7 May 24 2022 02:38:47

%S 1,2,9,41,1313,5471,1181737,28952557,1235309099,150090055529,

%T 30018011105801,201787741322329,523033825507476769,

%U 44196358255381786981,5774990812036553498851,1949059399062336805862213,997918412319916444601453057,3697415655903280160125896583

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

%F Numerators 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}] // Numerator

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

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

%K nonn,frac

%O 0,2

%A _Ilya Gutkovskiy_, May 23 2022