A346409 a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k)^2 * k!).

0, 1, -3, 13, -52, 476, 1344, 156192, 6935424, 470168064, 38948065920, 3979380286080, 489922581219840, 71586095491054080, 12249193741572372480, 2426646293132502067200, 551096248249459158220800, 142236660450422499604070400, 41404182857569072540171468800

Offset: 0

Author

Ilya Gutkovskiy, Jul 15 2021

Keywords

• sign

Crossrefs

Cf. A002741, A009940, A082491, A142999, A346405.

Programs

Mathematica

Table[(n!)^2 Sum[(-1)^k/((n - k)^2 k!), {k, 0, n - 1}], {n, 0, 18}]
nmax = 18; CoefficientList[Series[PolyLog[2, x] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!^2

Formula

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