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

0,3

Links

Table of n, a(n) for n=0..19.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * BesselJ(0,2*sqrt(x)).

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

Crossrefs

Cf. A002741, A073701, A336292, A340789, A346410.

Sequence in context: A270107 A100231 A016609 * A199618 A088745 A213922

Adjacent sequences: A346408 A346409 A346410 * A346412 A346413 A346414

Keyword

sign

Author

Ilya Gutkovskiy, Jul 15 2021

Status

approved