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%I #12 Jan 20 2024 17:24:08
%S 1,1,3,11,62,442,3892,40504,487496,6655688,101656592,1717234432,
%T 31789038304,639932442976,13918144177088,325239867277952,
%U 8126648153635712,216210586758515584,6102238859442194176,182102977877507458048,5729025247479379569152
%N a(0)=a(1)=1, a(2)=3, thereafter a(n) = n*a(n-1)+(n-1)*(n-2)*a(n-2).
%H Harvey P. Dale, <a href="/A291287/b291287.txt">Table of n, a(n) for n = 0..417</a>
%H Tomislav Doslic and R. Sharafdini, <a href="https://doi.org/10.1007/978-3-319-31584-3_10">Hosoya Index of Splices, Bridges, and Necklaces</a>, in Distance, Symmetry, and Topology in Carbon Nanomaterials, 2016, pp 147-156. Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9), doi:10.1007/978-3-319-31584-3_10. See the end of Section 2 (page 9).
%p f:=proc(n) option remember;
%p if n <= 1 then 1 elif n=2 then 3 else
%p n*f(n-1)+(n-1)*(n-2)*f(n-2); fi; end;
%p [seq(f(n),n=0..20)];
%t nxt[{n_,a_,b_}]:={n+1,b,b(n+1)+n(n-1)a}; Join[{1},NestList[nxt,{2,1,3},20][[;;,2]]] (* _Harvey P. Dale_, Jan 20 2024 *)
%Y Cf. A244430, A291286.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Aug 27 2017
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