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Number of spanning trees of the n-barbell graph.
1

%I #24 Feb 16 2025 08:33:15

%S 1,1,1,9,256,15625,1679616,282475249,68719476736,22876792454961,

%T 10000000000000000,5559917313492231481,3833759992447475122176,

%U 3211838877954855105157369,3214199700417740936751087616,3787675244106352329254150390625

%N Number of spanning trees of the n-barbell graph.

%C a(n) = A000272(n)^2 for n>=0.

%H M. F. Hasler, <a href="/A193129/b193129.txt">Table of n, a(n) for n = 0..32</a> (corrected by _Georg Fischer_, Jan 20 2019)

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BarbellGraph.html">Barbell Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>

%F a(0)=1 and a(n)=n^(2n-4) for n>=1 (from the comment and the formula for A000272).

%t Table[n^(2 n - 4), {n, 3, 20}]

%o (PARI) A193129=n^(2*n-4) \\ _M. F. Hasler_, Apr 14 2015

%Y Cf. A000272.

%K nonn,changed

%O 0,4

%A _Eric W. Weisstein_, Jul 16 2011