A346411 a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k) * k!)^2.
0, 1, -3, 4, -8, 1, 353, 27224, 1871840, 147012849, 13684928021, 1514370713340, 197964773810648, 30300949591876913, 5380510834911767033, 1098630080602791984784, 255851291397441057781120, 67450889282916741495608737, 19994198644782014829579657837, 6623096362909598587714211804212
Offset: 0
Keywords
Programs
-
Mathematica
Table[(n!)^2 Sum[(-1)^k/((n - k) k!)^2, {k, 0, n - 1}], {n, 0, 19}] nmax = 19; CoefficientList[Series[PolyLog[2, x] BesselJ[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
Formula
Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * BesselJ(0,2*sqrt(x)).