A329052 Array read by antidiagonals: T(n,m) is the number of unlabeled bicolored acyclic graphs with n nodes of one color and m of the other.
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 21, 15, 6, 1, 1, 7, 21, 38, 38, 21, 7, 1, 1, 8, 28, 62, 82, 62, 28, 8, 1, 1, 9, 36, 95, 158, 158, 95, 36, 9, 1, 1, 10, 45, 138, 278, 356, 278, 138, 45, 10, 1, 1, 11, 55, 192, 459, 724, 724, 459, 192, 55, 11, 1
Offset: 0
Examples
Array begins: ======================================================= n\m | 0 1 2 3 4 5 6 7 8 ----+-------------------------------------------------- 0 | 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1 | 1, 2, 3, 4, 5, 6, 7, 8, 9, ... 2 | 1, 3, 6, 10, 15, 21, 28, 36, 45, ... 3 | 1, 4, 10, 21, 38, 62, 95, 138, 192, ... 4 | 1, 5, 15, 38, 82, 158, 278, 459, 716, ... 5 | 1, 6, 21, 62, 158, 356, 724, 1359, 2388, ... 6 | 1, 7, 28, 95, 278, 724, 1690, 3612, 7143, ... 7 | 1, 8, 36, 138, 459, 1359, 3612, 8731, 19404, ... 8 | 1, 9, 45, 192, 716, 2388, 7143, 19404, 48213, ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325
Crossrefs
Programs
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PARI
EulerXY(A)={my(j=serprec(A,x)); exp(sum(i=1, j, 1/i * subst(subst(A + x * O(x^(j\i)), x, x^i), y, y^i)))} R(n)={my(A=O(x)); for(j=1, 2*n, A = if(j%2, 1, y)*x*EulerXY(A)); A}; P(n)={my(r1=R(n), r2=x*EulerXY(r1), s=r1+r2-r1*r2); Vec(EulerXY(s))} { my(A=P(10)); for(n=0, #A\2, for(k=0, #A\2, print1(polcoef(A[n+k+1], k), ", ")); print) }
Comments