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 A380622 #9 Jan 29 2025 16:35:34
%S A380622 1,1,0,1,1,1,1,0,1,0,1,3,5,1,0,1,0,24,0,1,0,1,15,189,297,60,1,0,1,0,
%T A380622 1695,0,4896,0,1,0,1,105,19305,472200,869400,100278,1105,1,0,1,0,
%U A380622 252000,0,242183775,0,2450304,0,1,0,1,945,3828825,2465608950,103694490900,198147676875,16482741030,69533397,27120,1,0
%N A380622 Array read by antidiagonals: T(n,k) is the number of rooted k-regular combinatorial maps with n vertices, n >= 0, k >= 1.
%C A380622 The combinatorial maps considered are connected, unlabeled, may have loops and parallel edges and are of any orientable genus.
%H A380622 Andrew Howroyd, <a href="/A380622/b380622.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals)
%F A380622 A380625(n) = Sum_{d|2*n} T(d,2*n/d).
%e A380622 Array begins:
%e A380622 ============================================================
%e A380622 n\k | 1 2 3 4 5 6 7 8 ...
%e A380622 ----+-------------------------------------------------------
%e A380622 0 | 1 1 1 1 1 1 1 1 ...
%e A380622 1 | 0 1 0 3 0 15 0 105 ...
%e A380622 2 | 1 1 5 24 189 1695 19305 252000 ...
%e A380622 3 | 0 1 0 297 0 472200 0 2465608950 ...
%e A380622 4 | 0 1 60 4896 869400 242183775 ...
%e A380622 5 | 0 1 0 100278 0 ...
%e A380622 6 | 0 1 1105 2450304 ...
%e A380622 7 | 0 1 0 ...
%e A380622 ...
%o A380622 (PARI) T(n,k)={my(A=O(x^(n*k+1)), g=serlaplace(serconvol(exp(x^k/k + A), exp(x^2/2 + A)))); polcoef(1 + x*deriv(g)/g, n*k)}
%Y A380622 Columns 2..6 are A000012, A062980 (with interspersed zeros), A292186, A380623 (with interspersed zeros), A380624.
%Y A380622 Cf. A053979, A269919, A380625.
%K A380622 nonn,tabl
%O A380622 0,12
%A A380622 _Andrew Howroyd_, Jan 29 2025