A380615 Triangle read by rows: T(n,k) is the number of sensed combinatorial maps with n edges and k vertices, 1 <= k <= n + 1.
1, 1, 1, 2, 2, 1, 5, 8, 5, 2, 18, 38, 34, 14, 3, 105, 275, 288, 154, 42, 6, 902, 2614, 3102, 1959, 705, 140, 14, 9749, 30346, 39242, 27898, 11956, 3142, 473, 34, 127072, 415360, 573654, 446078, 217000, 68544, 13886, 1670, 95, 1915951, 6513999, 9484003, 7911844, 4230802, 1523176, 373188, 60614, 5969, 280
Offset: 0
Examples
Triangle begins: n\k | 1 2 3 4 5 6 7 8 9 ----+---------------------------------------------------------------- 0 | 1 1 | 1, 1 2 | 2, 2, 1; 3 | 5, 8, 5, 2; 4 | 18, 38, 34, 14, 3; 5 | 105, 275, 288, 154, 42, 6; 6 | 902, 2614, 3102, 1959, 705, 140, 14; 7 | 9749, 30346, 39242, 27898, 11956, 3142, 473, 34; 8 | 127072, 415360, 573654, 446078, 217000, 68544, 13886, 1670, 95; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
Crossrefs
Programs
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PARI
InvEulerMTS(p)={my(n=serprec(p, x)-1, q=log(p), vars=variables(p)); sum(i=1, n, moebius(i)*substvec(q + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i)} 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,y)={my(p=sumdiv(k,d,eulerphi(k/d)*y^d)/k); sum(i=0, r, abs(stirling(r,i,1))*p^i)/r!} S(n,k,y)={sum(r=0, 2*n\k, if(k*r%2==0, x^(k*r/2)*b(k,r)*C(k,r,y)), O(x*x^n))} G(n,y='y)={prod(k=1, 2*n, S(n,k,y))} T(n)={[Vecrev(p/y) | p<-Vec(y+InvEulerMTS(G(n)))]} { my(A=T(10)); for(i=1, #A, print(A[i])) }
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