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A342557
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T(n,m) is the number of unlabeled connected graphs without endpoints on m nodes with n edges, where T(n,m), m <= n, is a triangle read by rows.
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5
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0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 3, 5, 1, 0, 0, 0, 0, 2, 11, 8, 1, 0, 0, 0, 0, 1, 15, 31, 12, 1, 0, 0, 0, 0, 1, 12, 63, 71, 16, 1, 0, 0, 0, 0, 0, 8, 89, 231, 144, 21, 1, 0, 0, 0, 0, 0, 5, 97, 513, 707, 274, 27, 1
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internal format)
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OFFSET
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1,20
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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The triangle begins
0;
0, 0;
0, 0, 1;
0, 0, 0, 1;
0, 0, 0, 1, 1;
0, 0, 0, 1, 3, 1;
0, 0, 0, 0, 3, 5, 1;
0, 0, 0, 0, 2, 11, 8, 1;
0, 0, 0, 0, 1, 15, 31, 12, 1;
0, 0, 0, 0, 1, 12, 63, 71, 16, 1;
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PROG
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(PARI) \\ Needs G() defined in A369932.
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)}
T(n)={my(r=Vec(InvEulerMTS(substvec(G(n), [x, y], [y, x])))); vector(#r-1, i, Vecrev(Pol(r[i+1]/y), i)) }
{ my(A=T(12)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Feb 07 2024
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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