OFFSET
1,10
COMMENTS
LINKS
Alois P. Heinz, Antidiagonals n = 1..100, flattened
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Wikipedia, Chromatic Polynomial
FORMULA
EXAMPLE
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, ...
0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, ...
3, 12, 30, 66, 138, 282, 570, ...
6, 78, 474, 2238, 9546, 38958, 155994, ...
10, 340, 4780, 46420, 385660, 2995540, 22666780, ...
15, 1095, 32955, 617775, 9248595, 123920295, 1569542955, ...
MAPLE
P:= proc(n) option remember;
unapply(expand(add(add(Stirling2(n, k) *Stirling2(n, m)
*mul(q-i, i=0..k+m-1) *(q-k-m)^n, m=1..n), k=1..n)), q)
end:
A:= (n, k)-> P(k)(n)/(2*n):
seq(seq(A(n, 1+d-n), n=1..d), d=1..12);
MATHEMATICA
p[n_] := p[n] = Function[q, Expand[Sum[Sum[StirlingS2[n, k] * StirlingS2[n, m] * Product[q-i, {i, 0, k+m-1}]*(q-k-m)^n, {m, 1, n}], {k, 1, n}]]]; a[n_, k_] := p[k][n]/(2*n); Table[Table[a[n, 1+d-n], {n, 1, d}], {d, 1, 12}] // Flatten (* Jean-François Alcover, Dec 13 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, May 06 2012
STATUS
approved