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

0,3

Links

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

Prog

(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)))))}

Crossrefs

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

Sequence in context: A256126 A321607 A024335 * A203009 A024336 A145144

Adjacent sequences: A380362 A380363 A380364 * A380366 A380367 A380368

Keyword

nonn,new

Author

Andrew Howroyd, Jan 28 2025

Status

approved