login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A189995 The order b_{4n-1} of the cyclic group S_{4n-1}^{bp} of oriented diffeomorphism classes of smooth homotopy (4n-1)-spheres that bound parallelizable manifolds, for n > 1. 3
28, 992, 8128, 261632, 1448424448, 67100672, 1941802827776, 753623571759104, 23998307331473408, 341653284209033216, 8316321134799694594048, 740764429532373450752, 30559446583872811817762816, 496669433444154134078771167232, 17776484020396435145889494859776, 11188223110510348416175908585472 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For a(n), Milnor 2011 Theorem 5 gives the formula

2^(2*n-2)*(2^(2*n-1)-1)*numerator(4*bernoulli(n)/n)

where bernoulli(n) = abs(Bernoulli(2*n)).

See A001676 for additional comments, references, and links.

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..235

John W. Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (2011), 804-809 (see Theorem 5 and Table 3).

John W. Milnor, Spheres, Abel Prize lecture (video), 2011.

FORMULA

a(n) = 2^(2*n - 2) * (2^(2*n - 1) - 1) * abs(numerator(4*Bernoulli(2*n)/n)).

a(n) = A187595(4*n-1) for n > 1.

EXAMPLE

a(2) = 2^2 * (2^3 - 1) * abs(numerator(4 * Bernoulli(4)/2)) = 4 * 7 * abs(numerator(2 * (-1/30)) = 28

MATHEMATICA

Table[2^(2*n-2)*(2^(2*n-1)-1)*Abs[Numerator[4*BernoulliB[2*n]/n]], {n, 2, 17}]

PROG

(MAGMA) [2^(2*n-2)*(2^(2*n-1)-1)*Abs(Numerator(4*Bernoulli(2*n)/n)): n in [2..30]]; // G. C. Greubel, Jan 11 2018

CROSSREFS

Cf. A001676, A047680, A057617, A187595, A228689.

Sequence in context: A097579 A091549 A034904 * A228689 A218480 A162006

Adjacent sequences:  A189992 A189993 A189994 * A189996 A189997 A189998

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Jun 15 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)