A005395 Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded up.

0, 1, 2, 6, 24, 119, 711, 4981, 39903, 359537, 3598696, 39615626, 475687487, 6187239476, 86661001741, 1300430722200, 20814114415224, 353948328666101, 6372804626194310, 121112786592293964, 2422786846761133394, 50888617325509644404, 1119751494628234263303

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..150

Wikipedia, Stirling's Approximation

Formula

a(n) = ceiling(sqrt(2*Pi)*n^(n+(1/2))/e^n). - Wesley Ivan Hurt, Jun 11 2016

Maple

A005395:=n->ceil(sqrt(2*Pi)*n^(n+(1/2))/exp(1)^n): seq(A005395(n), n=0..30); # Wesley Ivan Hurt, Jun 11 2016

Mathematica

Table[Ceiling[Sqrt[2*Pi]*n^(n + (1/2))/E^n], {n, 0, 20}] (* Wesley Ivan Hurt, Jun 11 2016 *)

Crossrefs

Cf. (rounded down) A005393.

Sequence in context: A202235 A202236 A177523 * A370383 A357920 A358611

Adjacent sequences: A005392 A005393 A005394 * A005396 A005397 A005398

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(12) onwards corrected by Sean A. Irvine, Jun 11 2016

Status

approved