A289830 a(n) satisfies the equation n/(n-1) + a(n)/n! = H(n), where H(n) is the n-th harmonic number.

-1, 2, 18, 124, 900, 7188, 63504, 618336, 6596640, 76635360, 963895680, 13056819840, 189581333760, 2938083321600, 48416639846400, 845487698227200, 15598004134809600, 303161985274982400, 6191998554470400000, 132599321499875328000, 2970952207377960960000

Offset: 2

Author

Joseph Wheat, Jul 12 2017

Keywords

• sign

Crossrefs

Cf. A001008, A002805.

Programs

Mathematica

Table[n!*(HarmonicNumber[n] - n/(n - 1)), {n, 2, 22}] (* Michael De Vlieger, Jul 13 2017 *)

Python

from sympy import factorial, harmonic
def a(n): return factorial(n-2)*(harmonic(n)*(n-1) - n)*n
print([a(n) for n in range(2, 26)]) # Indranil Ghosh, Jul 14 2017

Formula

a(n) = n! * (H(n) - n/(n-1)). - Alois P. Heinz, Jul 13 2017

Extensions

More terms from Alois P. Heinz, Jul 13 2017