The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A056545 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A056545

a(n) = 4*n*a(n-1) + 1 with a(0)=1.
(history; published version)

#41 by Hugo Pfoertner at Thu Aug 15 06:40:13 EDT 2024

STATUS

reviewed

approved

#40 by Joerg Arndt at Thu Aug 15 06:19:18 EDT 2024

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proposed

reviewed

#39 by Jason Yuen at Thu Aug 15 04:09:26 EDT 2024

STATUS

editing

proposed

#38 by Jason Yuen at Thu Aug 15 04:09:08 EDT 2024

FORMULA

a(n) = n!*Sum_{k=0..n} (4^(n-k)/k!.

STATUS

approved

editing

#37 by Harvey P. Dale at Tue Mar 19 16:52:33 EDT 2019

STATUS

editing

approved

#36 by Harvey P. Dale at Tue Mar 19 16:52:28 EDT 2019

LINKS

Harvey P. Dale, <a href="/A056545/b056545.txt">Table of n, a(n) for n = 0..365</a>

STATUS

approved

editing

#35 by Harvey P. Dale at Tue Mar 19 16:49:55 EDT 2019

STATUS

editing

approved

#34 by Harvey P. Dale at Tue Mar 19 16:49:50 EDT 2019

MATHEMATICA

nxt[{n_, a_}]:={n+1, 4a(n+1)+1}; NestList[nxt, {0, 1}, 20][[All, 2]] (* Harvey P. Dale, Mar 19 2019 *)

STATUS

approved

editing

#33 by Bruno Berselli at Thu Mar 02 06:02:56 EST 2017

STATUS

editing

approved

#32 by Bruno Berselli at Thu Mar 02 06:02:44 EST 2017

FORMULA

a(n) = floor( e^(1/4)*4^n*n! ).

From Philippe Deléham, Mar 14 2004: (Start)

a(n) = n!*sumSum_{k=0..n} (4^(n-k)/k!, k=0..n). - _Philippe Deléham_, Mar 14 2004

E.g.f.: exp(x)/(1 - 4*x). - _Philippe Deléham_, Mar 14 2004(End)

a(n) = Sum[_{k=0..n} P(n, k)*4^k, {k, 0, n}]. - Ross La Haye, Aug 29 2005

KEYWORD

easy,nonn,easy,changed

STATUS

proposed

editing