A163585 a(n) = floor((4*Pi)^n * n!).

1, 12, 315, 11906, 598481, 37603698, 2835252098, 249401800589, 25072603664742, 2835644669262813, 356337618445884526, 49256576349520039506, 7427716723230571769719, 1213412735113655221460574, 213474717926699991459606943, 40239036333940441855233097277

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..314

S.-S. Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math. (2) 45 (1944) 747-752.

Formula

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

Example

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

Mathematica

Table[Floor[4^n*(Pi^n)*n!], {n, 0, 50}] (* G. C. Greubel, Jul 28 2017 *)

Prog

(PARI) A163585(n)={ floor((4*Pi)^n*n!) }
{ realprecision=120 ; for(n=1, 20, print1(A163585(n), ", ") ; ); } \\ R. J. Mathar, Aug 07 2009
(Python)
from mpmath import mp, pi, fac
mp.dps = 120
def a(n): return int(floor((4*pi)**n*fac(n)))
print([a(n) for n in range(21)]) # Indranil Ghosh, Jul 28 2017

Crossrefs

Cf. A000142, A000302, A000796.

Sequence in context: A060010 A129583 A323839 * A341185 A279293 A180790

Adjacent sequences: A163582 A163583 A163584 * A163586 A163587 A163588

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 31 2009

Extensions

More terms from R. J. Mathar, Aug 07 2009

New name using formula, Joerg Arndt, Jul 30 2017

Status

approved