A346291 a(0) = 1; a(n) = (1/n) * Sum_{k=2..n} (binomial(n,k) * k!)^2 * a(n-k) / k.
1, 0, 1, 4, 54, 976, 27050, 1037016, 53040344, 3494603904, 288738690552, 29267185135200, 3573720291756912, 517691602686711168, 87813773085480166608, 17246816939881695262656, 3883816372280829757142400, 994217196872849143760818176, 287129874355801742457562921344
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = (1/n) Sum[(Binomial[n, k] k!)^2 a[n - k]/k, {k, 2, n}]; Table[a[n], {n, 0, 18}] nmax = 18; CoefficientList[Series[Exp[PolyLog[2, x] - x], {x, 0, nmax}], x] Range[0, nmax]!^2
Formula
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( polylog(2,x) - x ).
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp( Sum_{n>=2} x^n / n^2 ).