The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A047680

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A047680

a(n) = 2^(2*n-2) * (2^(2*n-1)-1) * numerator(|Bernoulli(4*n)|/n).
(history; published version)

#25 by N. J. A. Sloane at Wed Nov 30 08:01:08 EST 2022

STATUS

proposed

approved

#24 by Andrey Zabolotskiy at Wed Nov 30 07:38:01 EST 2022

STATUS

editing

proposed

#23 by Andrey Zabolotskiy at Wed Nov 30 07:37:46 EST 2022

CROSSREFS

Cf. A189995 (similar formula).

#22 by Andrey Zabolotskiy at Wed Nov 30 07:37:24 EST 2022

LINKS

<a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>

STATUS

proposed

editing

#21 by Jon E. Schoenfield at Wed Nov 30 06:54:09 EST 2022

STATUS

editing

proposed

Discussion

Wed Nov 30

07:29

N. J. A. Sloane: Why did you delete the three references?  Two are where I found the sequence, and one is because it involves the Bernoulli numbers.  Please restore them. Also you should mention that the connection with A189935.

07:37

Andrey Zabolotskiy: No, this sequence is not in these two references -- neither the terms nor the formula (A189995 is in these references). As for the Bernoulli numbers index entry, yes, my bad, thanks.

#20 by Jon E. Schoenfield at Wed Nov 30 06:54:06 EST 2022

NAME

a(n) = 2^(2*n-2) * (2^(2*n-1)-1) * numerator(|bernoulliBernoulli(4*n)|/n).

STATUS

proposed

editing

#19 by Michel Marcus at Wed Nov 30 05:46:17 EST 2022

STATUS

editing

proposed

#18 by Michel Marcus at Wed Nov 30 05:45:21 EST 2022

PROG

(PARI) a(n) = 2^(2*n-2) * (2^(2*n-1)-1) * numerator(abs(bernfrac(4*n))/n); \\ Michel Marcus, Nov 30 2022

STATUS

proposed

editing

#17 by Andrey Zabolotskiy at Wed Nov 30 04:58:17 EST 2022

STATUS

editing

proposed

#16 by Andrey Zabolotskiy at Wed Nov 30 04:57:03 EST 2022

NAME

Order of cyclic group of diffeomorphism classes of exotic (4n-1)-spheres which bound parallelizable manifolds, for n >= 2.

a(n) = 2^(2*n-2) * (2^(2*n-1)-1) * numerator(|bernoulli(4*n)|/n).

COMMENTS

Is this an erroneous version of A189995? - Andrey Zabolotskiy, Nov 29 2022

REFERENCES

J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton, 1974, p. 285.

LINKS

John W. Milnor, <a href="http://www.ams.org/notices/201106/rtx110600804p.pdf">Differential Topology Forty-six Years Later</a>, Notices Amer. Math. Soc. 58 (2011), 804-809.

<a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers</a>.

CROSSREFS

Cf. A001676A189995.

EXTENSIONS

Edited by Andrey Zabolotskiy, Nov 30 2022

STATUS

proposed

editing