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

%I A380365 #7 Jan 28 2025 15:28:52
%S A380365 1,1,3,11,50,365,3782,47935,718202,12245679,233541489,4920828395,
%T A380365 113495838798,2843930973805,76932818058660,2234631397864123,
%U A380365 69368177318863458,2291843543825994905,80296746074069588380,2973657775519950500203,116065360915389313936460
%N A380365 Number of sensed combinatorial maps with n edges and without faces of degree 1.
%H A380365 Andrew Howroyd, <a href="/A380365/b380365.txt">Table of n, a(n) for n = 0..200</a>
%o A380365 (PARI)
%o A380365 InvEulerT(v)={dirdiv(Vec(log(1+x*Ser(v)),-#v), vector(#v,n,1/n))}
%o A380365 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)))}
%o A380365 C(k,r)={sum(i=0, r, (-1)^i/i!/k^i)}
%o A380365 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))}
%o A380365 seq(n)={concat([1], InvEulerT(Vec(-1 + prod(k=1, 2*n, S(n,k)))))}
%Y A380365 Cf. A006388 (planar), A170946, A380364 (rooted), A380366 (unsensed).
%K A380365 nonn
%O A380365 0,3
%A A380365 _Andrew Howroyd_, Jan 28 2025