A346405 - OEIS

%I #5 Jul 15 2021 21:21:08

%S 0,1,5,31,268,3476,70656,2202432,98622336,5954736384,463100042880,

%T 44924476970880,5308404719823360,749930460864929280,

%U 124754522068412651520,24129984694192721971200,5368254991077002482483200,1360938718277588430567014400,389980903967231535140578099200

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

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

%t Table[(n!)^2 Sum[1/((n - k)^2 k!), {k, 0, n - 1}], {n, 0, 18}]

%t nmax = 18; CoefficientList[Series[PolyLog[2, x] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!^2

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jul 15 2021