The On-Line Encyclopedia of Integer Sequences (OEIS)

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Revision History for A080227

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Showing entries 1-10 | older changes

A080227

a(n) = n*a(n-1) + (1/2)*(1+(-1)^n), a(0)=0.
(history; published version)

#24 by Michael De Vlieger at Mon Mar 27 07:51:06 EDT 2023

STATUS

reviewed

approved

#23 by Alois P. Heinz at Mon Mar 27 07:49:20 EDT 2023

STATUS

proposed

reviewed

#22 by Andrew Howroyd at Sun Mar 26 15:18:40 EDT 2023

STATUS

editing

proposed

#21 by Andrew Howroyd at Sun Mar 26 15:18:33 EDT 2023

FORMULA

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

a(n) = (n-1)*(a(n-1) + a(n-2)) + 1, for n > 1. - Gary Detlefs, Jun 22 2010

a(n) = (1/2)*(exp(-1)*Gamma(n+1,-1) + exp(1)*Gamma(n+1,1)) - Gamma(n+1,0). - Martin Clever, Mar 26 2023

STATUS

proposed

editing

#20 by Andrew Howroyd at Sun Mar 26 15:12:35 EDT 2023

STATUS

editing

proposed

#19 by Andrew Howroyd at Sun Mar 26 15:12:10 EDT 2023

CROSSREFS

Cf. A009179.

STATUS

proposed

editing

#18 by Martin Clever at Sun Mar 26 13:02:18 EDT 2023

STATUS

editing

proposed

Discussion

Sun Mar 26

13:04

Omar E. Pol: Needs cross-references.

13:08

Michel Marcus: like what ?

13:33

Martin Clever: It'a an explicit formula, it can be checked by substituting into the recursion equation.

15:02

Andrew Howroyd: Martin, not your formula. Omar is meaning the sequence itself has no cross-references. (which is not your problem, but something editors may want to address)

#17 by Martin Clever at Sun Mar 26 13:02:07 EDT 2023

FORMULA

a(n) = (1/2)*(exp(-1)*Gamma(n+1,-1)+exp(1)*Gamma(n+1,1))-Gamma(n+1,0). - Martin Clever, Mar 26 2023

STATUS

approved

editing

#16 by Alois P. Heinz at Thu Apr 13 11:08:50 EDT 2017

STATUS

editing

approved

#15 by Alois P. Heinz at Thu Apr 13 11:08:47 EDT 2017

DATA

0, 0, 1, 3, 13, 65, 391, 2737, 21897, 197073, 1970731, 21678041, 260136493, 3381774409, 47344841727, 710172625905, 11362762014481, 193166954246177, 3477005176431187, 66063098352192553, 1321261967043851061, 27746501307920872281, 610423028774259190183

STATUS

approved

editing