A127585 Exponential error term from Stirling's Approximation.

1, 1, 18, 345, 10243, 437769, 25260317, 1873346813, 172254143084, 19114537903943, 2506628271002200, 382005168783773474, 66734799966312471195, 13212509243902296154744, 2936153006332857671962341, 726345521215072990990045577, 198595552305314906351047196508

Offset: 0

Author

Jonathan Vos Post, Apr 02 2007

Keywords

• easy
• nonn

Examples

			a(1) = Floor[(sqrt(2*pi) * (1^1) * (1^(1/2))) - 1! ] = Floor(1.50662827) = 1.
a(2) = Floor[(sqrt(2*pi) * (2^2) * (2^(2/2))) - 2! ] = Floor(18.0530262) = 18.
		

Links

• Eric Weisstein's World of Mathematics, Stirling's Series.
• Eric Weisstein's World of Mathematics, Stirling's Approximation.

Crossrefs

Cf. A005394, A046968, A046969, A055775, A127426.

Formula

a(n) = floor(sqrt(2*Pi)*(n^n)*(n^(n/2))) - n!.

Extensions

More terms from Alois P. Heinz, Jan 24 2024