The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A007696

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A007696

Quartic (or 4-fold) factorial numbers: a(n) = Product_{k = 0..n-1} (4*k + 1).
(history; published version)

#134 by Peter Luschny at Fri Mar 08 11:55:11 EST 2024

STATUS

editing

approved

#133 by Peter Luschny at Fri Mar 08 11:54:41 EST 2024

COMMENTS

a(n) is the product of the positive integers k <= 4*n that have k == 1 (modulo 4). - Peter Luschny, Jun 23 2011

STATUS

approved

editing

Discussion

Fri Mar 08

11:55

Peter Luschny: I think this comment can go.

#132 by Joerg Arndt at Sun Dec 18 02:25:11 EST 2022

STATUS

reviewed

approved

#131 by Michel Marcus at Sun Dec 18 02:21:28 EST 2022

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proposed

reviewed

#130 by Amiram Eldar at Sun Dec 18 01:19:43 EST 2022

STATUS

editing

proposed

#129 by Amiram Eldar at Sun Dec 18 00:26:49 EST 2022

LINKS

W. Wolfdieter Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seq. 3 (2000), Article 00.2.4.

M. Maxie D. Schmidt, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Schmidt/multifact.html">Generalized j-Factorial Functions, Polynomials, and Applications </a>, J. Integer Seq. 13 (2010), Article 10.6.7; see page 39.

FORMULA

Sum_{n>=0} 1/a(n) = 1 + exp(1/4)*(Gamma(1/4) - Gamma(1/4, 1/4))/(2*sqrt(2)). - Amiram Eldar, Dec 18 2022

STATUS

approved

editing

#128 by Charles R Greathouse IV at Thu Sep 08 08:44:35 EDT 2022

PROG

(MAGMAMagma) [n le 2 select 1 else (4*(n-1)-7)*(Self(n-1) + 4*Self(n-2)): n in [1..20]]; // G. C. Greubel, Aug 15 2019

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#127 by Bruno Berselli at Fri Feb 14 06:36:26 EST 2020

STATUS

proposed

approved

#126 by R. J. Mathar at Fri Feb 14 05:24:01 EST 2020

STATUS

editing

proposed

#125 by R. J. Mathar at Fri Feb 14 05:23:56 EST 2020

FORMULA

D-finite with recurrence: a(n) = (16*n - 28) * a(n-2) + (4*n - 7) * a(n-1) for n >= 2. - Ivan N. Ianakiev, Aug 10 2013

D-finite with recurrence: a(n) +(-4*n+3)*a(n-1)=0, n>=1. - R. J. Mathar, Feb 14 2020

STATUS

approved

editing