The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000023

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A000023

Expansion of e.g.f. exp(-2*x)/(1-x).
(history; published version)

#123 by Alois P. Heinz at Sat May 20 07:10:23 EDT 2023

STATUS

editing

approved

#122 by Alois P. Heinz at Sat May 20 07:10:19 EDT 2023

FORMULA

a(n) = Sum_{k=0..n} A008290(n, k)*(-1)^k. - Philippe Deléham, Dec 15 2003

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approved

editing

#121 by Peter Luschny at Tue May 10 14:05:09 EDT 2022

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editing

approved

#120 by Peter Luschny at Tue May 10 14:04:59 EDT 2022

FORMULA

a(n) = KummerU(-n, -n, -2). - Peter Luschny, May 10 2022

MAPLE

a := n -> n!*sumadd(((-2)^k/k!), k=0..n): seq(a(n), n=0..27); # Zerinvary Lajos, Jun 22 2007

seq(simplify(KummerU(-n, -n, -2)), n = 0..22); # Peter Luschny, May 10 2022

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approved

editing

#119 by N. J. A. Sloane at Sun Aug 08 11:34:42 EDT 2021

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reviewed

approved

#118 by Joerg Arndt at Sun Aug 08 01:37:45 EDT 2021

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proposed

reviewed

#117 by Michel Marcus at Sun Aug 08 00:23:16 EDT 2021

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editing

proposed

#116 by Michel Marcus at Sun Aug 08 00:23:11 EDT 2021

FORMULA

D-finite with recurrence : - a(n) + (n-2)*a(n-1) + 2*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 14 2011

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proposed

editing

#115 by Jon E. Schoenfield at Sat Aug 07 20:33:13 EDT 2021

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proposed

#114 by Jon E. Schoenfield at Sat Aug 07 20:33:11 EDT 2021

FORMULA

D-finite with recurrence - a(n) + (n-2)*a(n-1) + 2*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 14 2011

E.g.f.: 1/E(0) where E(k) = 1 - x/(1-2/(2-(k+1)/E(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011

G.f.: 1/Q(0), where Q(k) = 1 + 2*x - x*(k+1)/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 19 2013

STATUS

approved

editing