A005450 Numerator of (1 + Gamma(n))/n.

2, 1, 1, 7, 5, 121, 103, 5041, 40321, 362881, 329891, 39916801, 36846277, 6227020801, 87178291201, 1307674368001, 1230752346353, 355687428096001, 336967037143579, 121645100408832001, 2432902008176640001

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 1..300
• Achilleas Sinefakopoulos, Problem 10578 (Submitted solution.)
• H. S. Wilf, Problem 10578, Amer. Math. Monthly, 104 (1997), 270.

Crossrefs

Cf. A005451 (denominators).

Programs

Magma

[Numerator((1 + Factorial(n-1))/n): n in [1..30]]; // G. C. Greubel, Nov 21 2022

Mathematica

Table[Numerator[(1 + Gamma[n])/n], {n, 50}] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Sep 12 2006 *)

SageMath

[numerator((1+gamma(n))/n) for n in range(1,31)] # G. C. Greubel, Nov 21 2022

Formula

Define b(n) = ( (n-1)*(n^2-3*n+1)*b(n-1) - (n-2)^3*b(n-2) )/(n*(n-3)); b(2) = b(3) = 1; a(n) = numerator(b(n)), since b(n)=(1+Gamma(n))/n. - Joseph Biberstine (jrbibers(AT)indiana.edu), Sep 12 2006

Extensions

Better description from Joseph Biberstine (jrbibers(AT)indiana.edu), Sep 12 2006