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Numerator of (1 + Gamma(n))/n.
3

%I #25 Nov 22 2022 21:41:42

%S 2,1,1,7,5,121,103,5041,40321,362881,329891,39916801,36846277,

%T 6227020801,87178291201,1307674368001,1230752346353,355687428096001,

%U 336967037143579,121645100408832001,2432902008176640001

%N Numerator of (1 + Gamma(n))/n.

%H G. C. Greubel, <a href="/A005450/b005450.txt">Table of n, a(n) for n = 1..300</a>

%H Achilleas Sinefakopoulos, <a href="https://web.archive.org/web/20010608193230/http://users.forthnet.gr/ath/asin/proandsol.htm">Problem 10578</a> (Submitted solution.)

%H H. S. Wilf, <a href="http://www.jstor.org/stable/2974795">Problem 10578</a>, Amer. Math. Monthly, 104 (1997), 270.

%F 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

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

%o (Magma) [Numerator((1 + Factorial(n-1))/n): n in [1..30]]; // _G. C. Greubel_, Nov 21 2022

%o (SageMath) [numerator((1+gamma(n))/n) for n in range(1,31)] # _G. C. Greubel_, Nov 21 2022

%Y Cf. A005451 (denominators).

%K nonn,frac

%O 1,1

%A _N. J. A. Sloane_

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