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 A380626 #8 Jan 29 2025 21:31:08
%S A380626 1,1,0,1,1,1,1,0,1,0,1,2,3,1,0,1,0,7,0,1,0,1,5,29,36,11,1,0,1,0,174,0,
%T A380626 365,0,1,0,1,18,1475,26614,44106,5250,81,1,0,1,0,16162,0,10107019,0,
%U A380626 103801,0,1,0,1,105,214215,102762168,3703659517,6605320523,549530780,2492164,1228,1,0
%N A380626 Array read by antidiagonals: T(n,k) is the number of sensed k-regular combinatorial maps with n vertices, n >= 0, k >= 1.
%C A380626 The combinatorial maps considered are connected, unrooted, unlabeled, may have loops and parallel edges and are of any orientable genus.
%H A380626 Andrew Howroyd, <a href="/A380626/b380626.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals)
%F A380626 A380629(n) = Sum_{d|2*n} T(d,2*n/d).
%e A380626 Array begins:
%e A380626 ==================================================================
%e A380626 n\k | 1 2 3 4 5 6 7 8 ...
%e A380626 ----+-------------------------------------------------------------
%e A380626 0 | 1 1 1 1 1 1 1 1 ...
%e A380626 1 | 0 1 0 2 0 5 0 18 ...
%e A380626 2 | 1 1 3 7 29 174 1475 16162 ...
%e A380626 3 | 0 1 0 36 0 26614 0 102762168 ...
%e A380626 4 | 0 1 11 365 44106 10107019 3703659517 ...
%e A380626 5 | 0 1 0 5250 0 6605320523 ...
%e A380626 6 | 0 1 81 103801 549530780 ...
%e A380626 7 | 0 1 0 2492164 ...
%e A380626 ...
%o A380626 (PARI)
%o A380626 InvEulerT(v)={dirdiv(Vec(log(1+x*Ser(v)),-#v), vector(#v,n,1/n))}
%o A380626 D(m,k)={my(g=gcd(m,k)); sumdiv(g, d, my(j=m/d); x^j*eulerphi(d)*k^(j-1)/j)}
%o A380626 G(n,m)={my(t=m*n); prod(k=1, t, my(A=O(x^(t\k+1)), p=serconvol(exp(A + D(m,k)), exp(A + D(2,k)))); sum(r=0, t\k, if(k*r%m==0, r!*polcoef(p,r)/(k^r)*x^(k*r/m)), O(x*x^n)) )}
%o A380626 T(n,k)=if(n==0, 1, InvEulerT(Vec(-1 + G(n,k), -n))[n])
%Y A380626 Columns 2..6 (odd columns with interspersed zeros) are A000012, A129114, A292206, A380627, A380628.
%Y A380626 Row n=1 is A007769 (with interspersed zeros).
%Y A380626 Cf. A170946, A380622 (rooted), A380629.
%K A380626 nonn,tabl
%O A380626 0,12
%A A380626 _Andrew Howroyd_, Jan 29 2025