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A005037 Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals rooted at a cell up to rotation.

%I A005037 M4236 #28 Aug 20 2019 03:19:18
%S A005037 1,1,6,40,285,2126,16380,129456,1043460,8544965,70893054,594610536,
%T A005037 5033644070,42952562100,369061673400,3190379997272,27727712947836,
%U A005037 242135589539124,2123541227823800,18695484623015200,165169213716082765
%N A005037 Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals rooted at a cell up to rotation.
%D A005037 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005037 Andrew Howroyd, <a href="/A005037/b005037.txt">Table of n, a(n) for n = 1..200</a>
%H A005037 F. Harary, E. M. Palmer, R. C. Read, <a href="/A000108/a000108_20.pdf">On the cell-growth problem for arbitrary polygons, computer printout, circa 1974</a>
%H A005037 F. Harary, E. M. Palmer and R. C. Read, <a href="http://dx.doi.org/10.1016/0012-365X(75)90041-2">On the cell-growth problem for arbitrary polygons</a>, Discr. Math. 11 (1975), 371-389.
%t A005037 u[n_, k_, r_] := r*Binomial[(k-1)*n + r, n]/((k-1)*n + r);
%t A005037 T[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;
%t A005037 a[n_] := T[n, 5];
%t A005037 Array[a, 21] (* _Jean-François Alcover_, Aug 20 2019, after _Andrew Howroyd_ *)
%Y A005037 Column k=5 of A295222.
%K A005037 nonn
%O A005037 1,3
%A A005037 _N. J. A. Sloane_
%E A005037 More terms from _Sean A. Irvine_, Mar 11 2016
%E A005037 Name edited by _Andrew Howroyd_, Nov 20 2017