A380365 Number of sensed combinatorial maps with n edges and without faces of degree 1.

1, 1, 3, 11, 50, 365, 3782, 47935, 718202, 12245679, 233541489, 4920828395, 113495838798, 2843930973805, 76932818058660, 2234631397864123, 69368177318863458, 2291843543825994905, 80296746074069588380, 2973657775519950500203, 116065360915389313936460

Offset: 0

Author

Andrew Howroyd, Jan 28 2025

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A006388 (planar), A170946, A380364 (rooted), A380366 (unsensed).

Programs

PARI

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)))))}