A380364
Number of rooted combinatorial maps with n edges and without faces of degree 1.
Original entry on oeis.org
1, 1, 4, 30, 284, 3240, 43282, 662760, 11446844, 220193310, 4669558564, 108251161920, 2723857695362, 73941952968000, 2154117314613604, 67038931862069790, 2219781607638887804, 77922680046440538600, 2890682855602209593362, 112998995448368143038120, 4642614436461699746566364
Offset: 0
-
seq(n)={my(A=O(x^(2*n+1)), g=serconvol(exp(x^2/2 + A),exp(-x + A)/(1-x))); Vec(substpol(1 + x*deriv(log(serlaplace(g))), x^2, x))}
A380365
Number of sensed combinatorial maps with n edges and without faces of degree 1.
Original entry on oeis.org
1, 1, 3, 11, 50, 365, 3782, 47935, 718202, 12245679, 233541489, 4920828395, 113495838798, 2843930973805, 76932818058660, 2234631397864123, 69368177318863458, 2291843543825994905, 80296746074069588380, 2973657775519950500203, 116065360915389313936460
Offset: 0
-
InvEulerT(v)={dirdiv(Vec(log(1+x*Ser(v)),-#v), vector(#v,n,1/n))}
b(k,r)={if(k%2, if(r%2, 0, my(j=r/2); k^j*(2*j)!/(j!*2^j)), sum(j=0, r\2, binomial(r, 2*j)*k^j*(2*j)!/(j!*2^j)))}
C(k,r)={sum(i=0, r, (-1)^i/i!/k^i)}
S(n,k)={sum(r=0, 2*n\k, if(k*r%2==0, x^(k*r/2)*b(k,r)*C(k,r)), O(x*x^n))}
seq(n)={concat([1], InvEulerT(Vec(-1 + prod(k=1, 2*n, S(n,k)))))}
Showing 1-2 of 2 results.