The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A260535 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A260535

a(n) = (2*n+1)!*Sum_{k=0..n} B(2*k), B(n) the n-th Bernoulli number.
(history; published version)

#6 by N. J. A. Sloane at Mon Sep 21 17:23:55 EDT 2015

STATUS

proposed

approved

#5 by Michael De Vlieger at Mon Sep 21 15:50:57 EDT 2015

STATUS

editing

proposed

Discussion

Mon Sep 21

16:04

Peter Luschny: Sure. I think that if a(n) is a fundamental mathematical sequence, then the sequence of the its partial sums is a natural object of study.

#4 by Michael De Vlieger at Mon Sep 21 15:50:36 EDT 2015

MATHEMATICA

Table[(2 n + 1)! Sum[BernoulliB[2 k], {k, 0, n}], {n, 0, 14}] (* Michael De Vlieger, Sep 21 2015 *)

STATUS

proposed

editing

#3 by Peter Luschny at Mon Sep 21 15:40:09 EDT 2015

STATUS

editing

proposed

Discussion

Mon Sep 21

15:47

Charles R Greathouse IV: To express surprise at the absence of a sequence is to suggest that it is natural. But I can't see why that would be the case here -- would you be so kind as to add some pointers for those of us who can't pierce the veil on their own?

#2 by Peter Luschny at Mon Sep 21 15:38:35 EDT 2015

NAME

allocated for Peter Luschnya(n) = (2*n+1)!*Sum_{k=0..n} B(2*k), B(n) the n-th Bernoulli number.

DATA

1, 7, 136, 5832, 407808, 47882880, 5893585920, 2763273139200, -1770980740300800, 6081299047511654400, -24479310471391641600000, 147692341217380307927040000, -1254349086918655739874508800000, 14641717268146696857494972006400000, -229475387530005564381034470860390400000

OFFSET

0,2

COMMENTS

It appears that for n > 6, a(n)*(-1)^n < 0. (This comment was inspired by an observation of Robert Israel in A061053.)

MAPLE

a := n -> (2*n+1)!*add(bernoulli(2*k), k=0..n): seq(a(n), n=0..30);

CROSSREFS

Cf. A061053.

KEYWORD

allocated

sign

AUTHOR

Peter Luschny, Sep 21 2015

STATUS

approved

editing

Discussion

Mon Sep 21

15:39

Peter Luschny: Is it time to say again: "I'm surprised that this sequence is not yet in the OEIS"? ;-)

#1 by Peter Luschny at Tue Jul 28 16:04:09 EDT 2015

NAME

allocated for Peter Luschny

KEYWORD

allocated

STATUS

approved