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A163585 a(n) = floor((4*Pi)^n * n!). 1
1, 12, 315, 11906, 598481, 37603698, 2835252098, 249401800589, 25072603664742, 2835644669262813, 356337618445884526, 49256576349520039506, 7427716723230571769719, 1213412735113655221460574, 213474717926699991459606943, 40239036333940441855233097277 (list; graph; refs; listen; history; text; internal format)
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.dps = 120

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

print map(a, range(21)) # Indranil Ghosh, Jul 28 2017

CROSSREFS

Cf. A000142, A000302, A000796.

Sequence in context: A060010 A129583 A323839 * A279293 A180790 A277072

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

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Last modified January 19 04:06 EST 2021. Contains 340262 sequences. (Running on oeis4.)