A163585 - OEIS

%I #30 Apr 24 2021 12:10:22

%S 1,12,315,11906,598481,37603698,2835252098,249401800589,

%T 25072603664742,2835644669262813,356337618445884526,

%U 49256576349520039506,7427716723230571769719,1213412735113655221460574,213474717926699991459606943,40239036333940441855233097277

%N a(n) = floor((4*Pi)^n * n!).

%H G. C. Greubel, <a href="/A163585/b163585.txt">Table of n, a(n) for n = 0..314</a>

%H S.-S. Chern, <a href="http://www.jstor.org/stable/1969302">A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds</a>, Ann. of Math. (2) 45 (1944) 747-752.

%F a(n) = floor((4*Pi)^n * n!).

%e a(5) = 37603698 = floor(2^(2 * 5) * Pi^5 * 120) = floor (37603698.9).

%t Table[Floor[4^n*(Pi^n)*n!], {n,0,50}] (* _G. C. Greubel_, Jul 28 2017 *)

%o (PARI) A163585(n)={ floor((4*Pi)^n*n!) }

%o { realprecision=120 ; for(n=1,20, print1(A163585(n),",") ; ); } \\ _R. J. Mathar_, Aug 07 2009

%o (Python)

%o from mpmath import mp, pi, fac

%o mp.dps = 120

%o def a(n): return int(floor((4*pi)**n*fac(n)))

%o print([a(n) for n in range(21)]) # _Indranil Ghosh_, Jul 28 2017

%Y Cf. A000142, A000302, A000796.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Jul 31 2009

%E More terms from _R. J. Mathar_, Aug 07 2009

%E New name using formula, _Joerg Arndt_, Jul 30 2017