A101611 a(n) = n! * Sum_{k=ceiling(n/2)..n} 1/k.

1, 3, 5, 26, 94, 684, 3828, 35664, 270576, 3068640, 29400480, 392722560, 4546558080, 69878833920, 948550176000, 16484477184000, 256697973504000, 4976250951168000, 87435019510272000, 1870345490614272000

Offset: 1

Author

Ralf Stephan, Dec 10 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A101609, A101610, A101612, A101613, A000254, A046673, A052517.

Programs

Mathematica

Rest@Table[CoefficientList[Series[(Log[1-x]-x*Log[1-x^2])/(x-1),{x, 0, 20}],x][[n]](n-1)!,{n, 1, 20}] (* Benedict W. J. Irwin, Apr 25 2017 *)

PARI

a(n) = n! * sum(k=ceil(n/2), n, 1/k); \\ Michel Marcus, Apr 25 2017

Python

import math
from sympy import factorial
def a(n): return factorial(n)*sum([1/k for k in range(int(math.ceil(n/2)), n + 1)]) # Indranil Ghosh, Apr 25 2017

Formula

E.g.f: (log(1 - x) - x*log(1 - x^2))/(x - 1). - Benedict W. J. Irwin, Apr 25 2017