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%I #13 May 30 2019 04:51:25
%S 16,80,666,6588,80886,1146916,18583160,337808300,6812539360,
%T 150922350288,3643698427650,95221941543232,2678117152113428,
%U 80658585770586368,2590036811212597862,88333886984966359596,3188853320209605353376,121480126482182314239216,4870248707151384381179450
%N Number of different (unlabeled) 2-cell embeddings of the n-wheel graph W_(n+1) on n+1 nodes into orientable surfaces.
%C Values of a(n) for n <= 3 are not well-defined.
%H B. P. Mull, R. G. Rieper and A. T. White, <a href="https://doi.org/10.1090/S0002-9939-1988-0938690-1">Enumerating 2-cell imbeddings of connected graphs</a>, Proc. Amer. Math. Soc. 103 (1988), 321-330.
%F a(n)=1/(2*n)*sum_(d|n) phi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1), n odd; a(n)=1/(2*n)*sum_(d|n) phi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1)+ 2^(n-3)*(n/2-1)!, n even, where phi(n) is the Euler totient function A000010.
%t f[n_] := Block[{d = Divisors[n], s}, s = Apply[Plus, EulerPhi[d]^2*2^(n/d)*(n/d - 1)!*d^(n/d - 1)]/(2n); If[ EvenQ[n], s = s + 2^(n - 3)*(n/2 - 1)! ]; s];
%o (PARI) a(n) = 1/(2*n)*sumdiv(n, d, eulerphi(d)^2*2^(n/d)*(n/d-1)!*d^(n/d-1)) + if (!(n % 2), 2^(n-3)*(n/2-1)!); \\ _Michel Marcus_, May 30 2019
%Y Cf. A000010, A069839.
%K nonn
%O 4,1
%A _Valery A. Liskovets_, Apr 22 2002
%E Edited and extended by _Robert G. Wilson v_ and _Vladeta Jovovic_, May 04 2002
%E More terms from _Michel Marcus_, May 30 2019
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