OFFSET
1,5
COMMENTS
T(n,k) is the number of blades of dimension (n-k) in the canonical basis of graduated blades (see Early link).
LINKS
G. C. Greubel, Rows n=1..100 of triangle, flattened
Nick Early, Honeycomb tessellations and canonical bases for permutohedral blades, arXiv:1810.03246 [math.CO], 2018.
EXAMPLE
Triangle begins:
1,
1, 1,
1, 4, 1,
1, 15, 9, 1,
1, 66, 66, 16, 1,
1, 365, 500, 190, 25, 1,
...
MATHEMATICA
T[n_, k_]:= Sum[StirlingS2[n, j]*Abs[StirlingS1[j-1, k-1]], {j, 1, n}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* G. C. Greubel, Oct 14 2018 *)
PROG
(PARI) T(n, k) = sum(i=1, n, stirling(n, i, 2)*abs(stirling(i-1, k-1, 1)));
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print);
(Magma) [[(&+[StirlingSecond(n, i)*Abs(StirlingFirst(i-1, k-1)): i in [1..n]]): k in [1..n]]: n in [1..10]]; // G. C. Greubel, Oct 14 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Oct 09 2018
STATUS
approved