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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, 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

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Last modified September 12 15:43 EDT 2024. Contains 375853 sequences. (Running on oeis4.)