OFFSET
1,5
COMMENTS
Equivalently, the number of ways to choose a stable partition of a simple connected graph on n labeled nodes with k parts. See A322064 for the definition of stable partition.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
FORMULA
T(n,k) = (1/k!)*Sum_{j=0..k} (-1)^(k-j)*binomial(k,j)*A322279(n,j).
EXAMPLE
Triangle begins:
1;
0, 1;
0, 3, 4;
0, 19, 84, 38;
0, 195, 2470, 3140, 728;
0, 3031, 108390, 307390, 186360, 26704;
0, 67263, 7192444, 42747460, 52630060, 18926544, 1866256;
...
PROG
(PARI)
M(n, K=n)={
my(p=sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n));
my(q=sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n));
my(W=vector(K, k, Col(serlaplace(log(serconvol(q, p^k))))));
Mat(vector(K, k, sum(i=1, k, (-1)^(k-i)*binomial(k, i)*W[i])/k!));
}
my(T=M(7)); for(n=1, #T, print(T[n, 1..n]))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Dec 01 2018
STATUS
approved