A291287 a(0)=a(1)=1, a(2)=3, thereafter a(n) = n*a(n-1)+(n-1)*(n-2)*a(n-2).
1, 1, 3, 11, 62, 442, 3892, 40504, 487496, 6655688, 101656592, 1717234432, 31789038304, 639932442976, 13918144177088, 325239867277952, 8126648153635712, 216210586758515584, 6102238859442194176, 182102977877507458048, 5729025247479379569152
Offset: 0
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..417
- Tomislav Doslic and R. Sharafdini, Hosoya Index of Splices, Bridges, and Necklaces, 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).
Programs
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Maple
f:=proc(n) option remember; if n <= 1 then 1 elif n=2 then 3 else n*f(n-1)+(n-1)*(n-2)*f(n-2); fi; end; [seq(f(n),n=0..20)];
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Mathematica
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 *)