Stepan Orevkov has authored 3 sequences.
A187014
Number of isomorphism classes of simply embedded (i.e., loop-free and without parallel edges bounding a disk) bipartite quadrangulations of RP^2 of minimum degree 3 with n nodes and n-1 faces.
Original entry on oeis.org
0, 0, 1, 2, 3, 7, 22, 57, 174, 554, 1848, 6291, 22052, 78361, 282420
Offset: 4
A187013
Number of isomorphism classes of simply embedded (i.e., loop-free and without parallel edges bounding a disk) quadrangulations of RP^2 of minimum degree 3 with n nodes and n-1 faces.
Original entry on oeis.org
1, 0, 2, 3, 6, 12, 37, 95, 293, 923, 3086, 10504, 36954, 131590, 475793
Offset: 4
A185650
a(n) is the number of rooted trees with 2n vertices n of whom are leaves.
Original entry on oeis.org
1, 2, 8, 39, 214, 1268, 7949, 51901, 349703, 2415348, 17020341, 121939535, 885841162, 6511874216, 48359860685, 362343773669, 2736184763500, 20805175635077, 159174733727167, 1224557214545788, 9467861087020239, 73534456468877012, 573484090227222260
Offset: 1
From _Gus Wiseman_, Nov 27 2022: (Start)
The a(1) = 1 through a(3) = 8 rooted trees:
(o) ((oo)) (((ooo)))
(o(o)) ((o)(oo))
((o(oo)))
((oo(o)))
(o((oo)))
(o(o)(o))
(o(o(o)))
(oo((o)))
(End)
This is the central column of
A055277.
For height = internals we have
A358587.
Square trees are counted by
A358589.
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terms = 23;
m = 2 terms;
T[, ] = 0;
Do[T[x_, z_] = z x - x + x Exp[Sum[Series[1/k T[x^k, z^k], {x, 0, j}, {z, 0, j}], {k, 1, j}]] // Normal, {j, 1, m}];
cc = CoefficientList[#, z]& /@ CoefficientList[T[x, z] , x];
Table[cc[[2n+1, n+1]], {n, 1, terms}] (* Jean-François Alcover, Sep 14 2018 *)
art[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[art/@c],OrderedQ],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[art[n],Count[#,{},{-2}]==n/2&]],{n,2,10,2}] (* Gus Wiseman, Nov 27 2022 *)
-
\\ here R is A055277 as vector of polynomials
R(n) = {my(A = O(x)); for(j=1, n, A = x*(y - 1 + exp( sum(i=1, j, 1/i * subst( subst( A + x * O(x^(j\i)), x, x^i), y, y^i) ) ))); Vec(A)};
{my(A=R(2*30)); vector(#A\2, k, polcoeff(A[2*k],k))} \\ Andrew Howroyd, May 21 2018
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