The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A272230

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A272230

E.g.f.: 2*exp(x)/(exp(2*x)+1+2*x).
(history; published version)

#26 by N. J. A. Sloane at Tue May 24 23:57:33 EDT 2016

STATUS

proposed

approved

#25 by Robert Israel at Tue May 24 17:36:54 EDT 2016

STATUS

editing

proposed

#24 by Robert Israel at Tue May 24 17:31:59 EDT 2016

LINKS

Robert Israel, <a href="/A272230/b272230.txt">Table of n, a(n) for n = 0..418</a>

MAPLE

S:= series(2*exp(x)/(exp(2*x)+1+2*x), x, 31):

seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, May 24 2016

STATUS

approved

editing

#23 by N. J. A. Sloane at Sun May 22 00:22:52 EDT 2016

STATUS

editing

approved

#22 by N. J. A. Sloane at Sun May 22 00:22:43 EDT 2016

FORMULA

a(n) = 1-2n*a(n-1)-Sum_{k=0..n-2}binomial(n,k)*2^(n-k-1)*a(k)

a(n) = Sum_{k=0..n} Sum_{j=0..k} Sum_{i=0..n} binomial(n,k)*binomial(k+i,i)*binomial(n,i)(i!*(-1)^(i+j)*(2j+1)^(n-i))/(2^k)

E.g.f.: 2*exp(x)/(exp(2*x)+1+2*x).

STATUS

proposed

editing

Discussion

Sun May 22

00:22

N. J. A. Sloane: edited

#21 by Christopher Ernst at Thu May 12 13:35:45 EDT 2016

STATUS

editing

proposed

#20 by Christopher Ernst at Thu May 12 13:34:58 EDT 2016

FORMULA

a(n)=Sum_{k=0..n}Sum_{j=0..k}Sum_{i=0..n}binomial(n,k)*binomial(k+i,i)*binomial(n,i)(i!*(-1)^(i+j)*(2j+1)^(n-i))/(2^k)

STATUS

proposed

editing

Discussion

Thu May 12

13:35

Christopher Ernst: Added the mathematica formula under the formula section per Michel Marcus's suggestion

#19 by Christopher Ernst at Thu May 12 13:25:48 EDT 2016

STATUS

editing

proposed

#18 by Christopher Ernst at Thu May 12 13:24:50 EDT 2016

COMMENTS

It appears that Empirically, for odd n, n|a(n) and for even n, (n-1)|a(n).

FORMULA

a(n)=1-2n*a(n-1)-Sum_{k=0..n-2}binomial(n,k)*2^(n-k-1)*a(k)

STATUS

proposed

editing

Discussion

Thu May 12

13:25

Christopher Ernst: I edited the comments per Danny Rorabaugh's reply and added a recurrence relation in the formula bar.

#17 by Vaclav Kotesovec at Tue May 03 04:36:54 EDT 2016

STATUS

editing

proposed

Discussion

Wed May 04

11:18

Michel Marcus: I think that the formula, on which the mathematica program is based, should be entered in the formula section

11:27

Christopher Ernst: Should recurrence relation formulas be added as well?  Should the formula be entered in terms of latex formatting?

Thu May 12

12:43

Danny Rorabaugh: I suggest replacing "It appears that for" with "Empirically, for" for the sake of anybody searching for open problems.

12:44

Danny Rorabaugh: Yes, if you have a recurrence, that goes into the Formula section. No, don't use LaTeX notation, but rather the standards found in http://oeis.org/wiki/Style_Sheet#Spelling_and_notation