A346405 a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k)^2 * k!).

0, 1, 5, 31, 268, 3476, 70656, 2202432, 98622336, 5954736384, 463100042880, 44924476970880, 5308404719823360, 749930460864929280, 124754522068412651520, 24129984694192721971200, 5368254991077002482483200, 1360938718277588430567014400, 389980903967231535140578099200

Offset: 0

Author

Ilya Gutkovskiy, Jul 15 2021

Keywords

• nonn

Crossrefs

Cf. A001819, A002104, A002720, A061573, A346409.

Programs

Mathematica

Table[(n!)^2 Sum[1/((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).