OFFSET
0,6
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
EXAMPLE
Triangle begins:
1;
0, 1;
0, 0, 3;
0, 0, 1, 16;
0, 0, 0, 15, 125;
0, 0, 0, 6, 222, 1296;
0, 0, 0, 1, 205, 3660, 16807;
0, 0, 0, 0, 120, 5700, 68295, 262144;
0, 0, 0, 0, 45, 6165, 156555, 1436568, 4782969;
...
MATHEMATICA
row[n_] := (SeriesCoefficient[#, {y, 0, n}]& /@ CoefficientList[ Log[Sum[x^k*(1+y)^Binomial[k, 2]/k!, {k, 0, n+1}]] + O[x]^(n+2), x]* Range[0, n+1]!) // Rest;
Table[row[n], {n, 0, 9}] // Flatten (* Jean-François Alcover, Aug 03 2022, after Andrew Howroyd *)
PROG
(PARI)
Row(n)={Vec(serlaplace(polcoef(log(O(x^2*x^n)+sum(k=0, n+1, x^k*(1 + y + O(y*y^n))^binomial(k, 2)/k!)), n, y)), -(n+1))}
{ for(n=0, 8, print(Row(n))) }
CROSSREFS
Main diagonal is A000272.
Subsequent diagonals give the number of connected labeled graphs with n nodes and n+k edges for k=0..11: A057500, A061540, A061541, A061542, A061543, A096117, A061544 A096150, A096224, A182294, A182295, A182371.
Row sums are A322137.
Column sums are A001187.
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 14 2021
STATUS
approved