cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A127610 a(n) = floor(( (n+1)/2 )^n) - n!.

Original entry on oeis.org

0, 0, 0, 2, 15, 123, 1118, 11344, 127831, 1590245, 21700716, 322880256, 5209007463, 90661989607, 1694616510154, 33876697720832, 721588072472639, 16321494271570569, 390811944752490542, 9878354899591168000, 262896868506265373394, 7349159002086450661211
Offset: 0

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Author

N. J. A. Sloane, Apr 03 2007

Keywords

Comments

Theorem (Cauchy): ((n+1)/2)^n > n! for n >= 2.

References

  • D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970; p. 192, 3.1.14.

Crossrefs

Cf. A127426.

Programs

A127585 Exponential error term from Stirling's Approximation.

Original entry on oeis.org

1, 1, 18, 345, 10243, 437769, 25260317, 1873346813, 172254143084, 19114537903943, 2506628271002200, 382005168783773474, 66734799966312471195, 13212509243902296154744, 2936153006332857671962341, 726345521215072990990045577, 198595552305314906351047196508
Offset: 0

Views

Author

Jonathan Vos Post, Apr 02 2007

Keywords

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.
		

Crossrefs

Formula

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

Extensions

More terms from Alois P. Heinz, Jan 24 2024

A369393 a(n) = 2^n*(((n + 1)/2)^n - n!).

Original entry on oeis.org

0, 0, 1, 16, 241, 3936, 71569, 1452032, 32724801, 814205440, 22221533401, 661258764288, 21336094568881, 742703018860544, 27764596902369825, 1110071630916222976, 47289995917566900481, 2139290897163297619968, 102449006445196880700841, 5179102933596854288384000, 275667346790825720172556401
Offset: 0

Views

Author

Hugo Pfoertner, Jan 24 2024

Keywords

Crossrefs

Showing 1-3 of 3 results.