This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380241 #14 Jan 22 2025 17:33:01 %S A380241 1,1,1,1,1,1,1,2,1,1,1,5,9,1,1,1,14,100,54,1,1,1,42,1225,3000,378,1,1, %T A380241 1,132,15876,171500,110000,2916,1,1,1,429,213444,10001880,30012500, %U A380241 4550000,24057,1,1,1,1430,2944656,591666768,7981500240,5987493750,204000000,208494,1,1 %N A380241 Array read by antidiagonals: T(n,k) is the number of rooted (2k)-regular planar maps with n vertices, n >= 0, k >= 0. %C A380241 The zeroth column is included by convention only for consistency with the first row sequences. %C A380241 The case for regular planar maps of odd valency is more complicated and without simple closed form formulas, so not presented in this sequence. See the references for additional information. %H A380241 Andrew Howroyd, <a href="/A380241/b380241.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals) %H A380241 E. A. Bender and E. R. Canfield, <a href="https://doi.org/10.1137/S089548019017765">The number of degree restricted rooted maps on the sphere</a>, SIAM J. Discrete Math. 7 (1994) 9-15. %H A380241 Zhicheng Gao and Mizan Rahman, <a href="https://doi.org/10.1007/BF02558463">Enumeration of k-poles</a>, Annals of Combinatorics 1 (1997), pp. 55-66. %H A380241 W. T. Tutte, <a href="https://doi.org/10.4153/CJM-1962-061-1">A Census of Slicings</a>, Canad. J. Math. 14 (1962), 708-722. %H A380241 W. T. Tutte, <a href="http://dx.doi.org/10.4153/CJM-1963-029-x">A Census of Planar Maps</a>, Canad. J. Math. 15 (1963), 249-271. %F A380241 T(n,k) = 2*binomial(2*k-1, k)^n*(n*k)!/(n!*(n*k - n + 2)!) for k > 0. %e A380241 Array begins: %e A380241 ==================================================================== %e A380241 n\k | 0 1 2 3 4 5 ... %e A380241 ----+--------------------------------------------------------------- %e A380241 0 | 1 1 1 1 1 1 ... %e A380241 1 | 1 1 2 5 14 42 ... %e A380241 2 | 1 1 9 100 1225 15876 ... %e A380241 3 | 1 1 54 3000 171500 10001880 ... %e A380241 4 | 1 1 378 110000 30012500 7981500240 ... %e A380241 5 | 1 1 2916 4550000 5987493750 7304332956480 ... %e A380241 6 | 1 1 24057 204000000 1302227368750 7310748066293952 ... %e A380241 7 | 1 1 208494 9690000000 301107909375000 7794097754539041792 ... %e A380241 ... %o A380241 (PARI) T(n,k)=if(k==0, 1, 2*binomial(2*k-1,k)^n*(n*k)!/(n!*(n*k - n + 2)!)) %Y A380241 Columns 0..3 are A000012 twice, A000168, A380242. %Y A380241 Rows 0..3 are A000012, A000108, A060150, A380243. %Y A380241 Cf. A269920. %K A380241 nonn,tabl %O A380241 0,8 %A A380241 _Andrew Howroyd_, Jan 22 2025