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%I #42 Sep 08 2022 08:44:52
%S 1,4,32,512,16384,1048576,134217728,34359738368,17592186044416,
%T 18014398509481984,36893488147419103232,151115727451828646838272,
%U 1237940039285380274899124224,20282409603651670423947251286016,664613997892457936451903530140172288
%N a(n) = 2^((n-1)*(n+2)/2).
%C Number of redundant paths for a fault-tolerant ATM switch.
%C Hankel transform (see A001906 for definition ) of A001850, A006139, A084601; also Hankel transform of the sequence 1, 0, 4, 0, 24, 0, 160, 0, 1120, ... (A059304 with interpolated zeros). - _Philippe Deléham_, Jul 03 2005
%C Hankel transform of A109980. Unsigned version of A127945. - _Philippe Deléham_, Dec 11 2008
%C a(n) = the multiplicative Wiener index of the wheel graph with n+3 vertices. The multiplicative Wiener index of a connected simple graph G is defined as the product of the distances between all pairs of distinct vertices of G. The wheel graph with n+3 vertices has (n+3)(n+2)/2 pairs of distinct vertices, of which 2(n+2) are adjacent; each of the remaining (n+2)(n-1)/2 pairs are at distance 2; consequently, the multiplicative Wiener index is 2^((n-1)(n+2)/2) = a(n). - _Emeric Deutsch_, Aug 17 2015
%H Vincenzo Librandi, <a href="/A036442/b036442.txt">Table of n, a(n) for n = 1..80</a>
%H P. Barry, <a href="http://arxiv.org/abs/1311.7161">Comparing two matrices of generalized moments defined by continued fraction expansions</a>, arXiv preprint arXiv:1311.7161, 2013 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Barry3/barry291.html">J. Int. Seq. 17 (2014) # 14.5.1</a>
%H P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H I. Gutman, W. Linert, I. Lukovits, and Z. Tomovic, <a href="http://dx.doi.org/10.1021/ci990060s">The multiplicative version of the Wiener index</a>, J. Chem. Inf. Comput. Sci., 40, 2000, 113-116.
%H C. Lo and C. Chiu, <a href="http://dx.doi.org/10.1109/LCN.1995.527326">A Fault-Tolerant Architecture for ATM Networks</a>, 20th IEEE Conf. Local Computer Networks, 1995, pp. 29-36
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(1) = 1, a(n) = a(n-1) * 2^n. - _Vincenzo Librandi_, Oct 24 2012
%t Table[2^((n-1) * (n+2)/2), {n, 1, 30}] (* _Vincenzo Librandi_, Oct 24 2012 *)
%o (Magma) I:=[1]; [n le 1 select I[n] else Self(n-1)*2^n: n in [1..20]]; // _Vincenzo Librandi_, Oct 24 2012
%o (PARI) a(n)=2^((n-1)*(n+2)/2) \\ _Charles R Greathouse IV_, Oct 24 2012
%o (Maxima) A036442[n]:=2^((n-1)*(n+2)/2)$
%o makelist(A036442[n],n,1,30); /* _Martin Ettl_, Oct 29 2012 */
%K easy,nonn
%O 1,2
%A Abdallah Rayhan (rayhan(AT)engr.uvic.ca)
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