Revision History for A166356
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#28 by Harvey P. Dale at Mon Apr 15 20:20:35 EDT 2024
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#27 by Harvey P. Dale at Mon Apr 15 20:20:33 EDT 2024
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| MATHEMATICA
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With[{nn=40}, Take[CoefficientList[Series[1+x ArcTanh[x], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Apr 15 2024 *)
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#26 by Alois P. Heinz at Sat May 20 14:46:06 EDT 2023
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#25 by Alois P. Heinz at Sat May 20 14:46:00 EDT 2023
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| DATA
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1, 2, 8, 144, 5760, 403200, 43545600, 6706022400, 1394852659200, 376610217984000, 128047474114560000, 53523844179886080000, 26976017466662584320000, 16131658445064225423360000, 11292160911544957796352000000, 9146650338351415815045120000000
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#24 by Jon E. Schoenfield at Sat May 20 14:29:33 EDT 2023
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#23 by Jon E. Schoenfield at Sat May 20 14:29:26 EDT 2023
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| COMMENTS
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For n>0, (4*n-1)*a(n) corresponds to the number of random walk labelings of the friendship graph F_n (i.e., the one-point union of n triangles). -_). - _Sela Fried_, May 20 2023
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Discussion
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| Sat May 20
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| Jon E. Schoenfield: (signature format corrected)
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#22 by Jon E. Schoenfield at Sat May 20 14:29:01 EDT 2023
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#21 by Jon E. Schoenfield at Sat May 20 14:28:58 EDT 2023
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| COMMENTS
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For n>0, (4*n-1)*a(n) corresponds to the number of random walk labelings of the friendship graph F_n (i.e. ., the one-point union of n triangles). -Sela Fried, May 20 2023
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| FORMULA
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E.g.f.: 1+ + x*arctanh(x) has expansion 1,, 0,, 2,, 0,, 8,, 0,, 144,..., ...
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#20 by Sela Fried at Sat May 20 14:16:20 EDT 2023
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#19 by Sela Fried at Sat May 20 14:16:16 EDT 2023
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| COMMENTS
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For n>0, (4*n-1)*a(n) corresponds to the number of random walk labelings of the friendship graph F_n (i.e. the one-point union of n triangles). -Sela Fried, May 20 2023
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| LINKS
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Sela Fried and Toufik Mansour, <a href="https://arxiv.org/abs/2305.09971">Further results on random walk labelings</a>, arXiv:2305.09971 [math.CO], 2023.
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