The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A007106 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A007106

Number of labeled odd degree trees with 2n nodes.
(history; published version)

#93 by Joerg Arndt at Mon Aug 22 04:49:41 EDT 2022

STATUS

reviewed

approved

#92 by Michel Marcus at Mon Aug 22 04:46:55 EDT 2022

STATUS

proposed

reviewed

#91 by Jon E. Schoenfield at Mon Aug 22 03:50:48 EDT 2022

STATUS

editing

proposed

#90 by Jon E. Schoenfield at Mon Aug 22 03:50:45 EDT 2022

LINKS

Math.Stackexchange.Com, Mathematics Stack Exchange, Marko R. Riedel, <a href="http://math.stackexchange.com/questions/1827737/">Odd degree trees</a>

Math.Stackexchange.Com, Mathematics Stack Exchange, Marko R. Riedel, <a href="http://math.stackexchange.com/questions/1104289/">Odd degree trees II</a>

STATUS

approved

editing

#89 by Peter Luschny at Sun May 08 04:42:01 EDT 2022

STATUS

proposed

approved

#88 by Peter Luschny at Sat May 07 15:20:59 EDT 2022

STATUS

editing

proposed

#87 by Peter Luschny at Sat May 07 15:20:41 EDT 2022

FORMULA

a(n) = Sum_{k=0..n-1} A156289(n-1, k)*Gamma(2*n+1)!/Gamma(2*n-k+1)!. - Peter Luschny, May 07 2022

STATUS

proposed

editing

#86 by Peter Luschny at Sat May 07 14:26:18 EDT 2022

STATUS

editing

proposed

#85 by Peter Luschny at Sat May 07 14:24:52 EDT 2022

DATA

1, 4, 96, 5888, 686080, 130179072, 36590059520, 14290429935616, 7405376630685696, 4917457306800619520, 4071967909087792857088, 4113850542422629363482624, 4980673081258443273955966976, 7119048451600750435732824260608, 11861520124846917915630931846103040

FORMULA

a(n) = Sum_{k=1..n} Cbinomial(n,k) * k! * (n-2)! [z^{n-2}] [u^k] exp(u(exp(z)+exp(-z)-2)/2)). - Marko Riedel, Jun 16 2016

a(n) = Sum_{k=0..n-1} A156289(n-1, k)*Gamma(2*n+1)/Gamma(2*n-k+1). - Peter Luschny, May 07 2022

CROSSREFS

Cf. A036778, A058014, A060279, A143601, A156289.

STATUS

proposed

editing

#84 by Marko Riedel at Sat May 07 13:06:06 EDT 2022

STATUS

editing

proposed