A342557 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.

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

Offset

1,20

Comments

The number of nonzero terms in the n-th row is A083920(n-1). - Hugo Pfoertner, Feb 01 2024

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50; first 24 rows from Hugo Pfoertner)

Formula

Bivariate inverse Euler transform of A369932. - Andrew Howroyd, Feb 07 2024

Example

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;

Prog

(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

Crossrefs

Cf. A004108 (column sums), A342556 (row sums).

Cf. A083920, A369932 (not necessarily connected).

Sequence in context: A059530 A193525 A049828 * A286131 A285631 A316836

Adjacent sequences: A342554 A342555 A342556 * A342558 A342559 A342560

Keyword

nonn,tabl

Author

Hugo Pfoertner, May 21 2021

Status

approved