

A285529


Triangle read by rows: T(n,k) is the number of nodes of degree k counted over all simple labeled graphs on n nodes, n>=1, 0<=k<=n1.


0



1, 2, 2, 6, 12, 6, 32, 96, 96, 32, 320, 1280, 1920, 1280, 320, 6144, 30720, 61440, 61440, 30720, 6144, 229376, 1376256, 3440640, 4587520, 3440640, 1376256, 229376, 16777216, 117440512, 352321536, 587202560, 587202560, 352321536, 117440512, 16777216
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Table of n, a(n) for n=1..36.


FORMULA

E.g.f. for column k: x * Sum_{n>=0} binomial(n,k)*2^binomial(n,2)*x^n/n!.
Sum_{k=1..n1} T(n,k)*k/2 = A095351(n).
T(n,k) = n*binomial(n1,k)*2^binomial(n1,2).  Alois P. Heinz, Apr 21 2017


EXAMPLE

1,
2, 2,
6, 12, 6,
32, 96, 96, 32,
320, 1280, 1920, 1280, 320,
...


MATHEMATICA

nn = 9; Map[Select[#, # > 0 &] &,
Drop[Transpose[Table[A[z_] := Sum[Binomial[n, k] 2^Binomial[n, 2] z^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[z A[z], {z, 0, nn}], z], {k, 0, nn  1}]], 1]] // Grid


CROSSREFS

Row sums give A095340.
Columns for k=03: A123903, A095338, A038094, A038096.
Sequence in context: A241669 A178802 A156992 * A305215 A219694 A054481
Adjacent sequences: A285526 A285527 A285528 * A285530 A285531 A285532


KEYWORD

nonn,tabl


AUTHOR

Geoffrey Critzer, Apr 20 2017


STATUS

approved



