A320280 Triangle T(n, k) = Sum_{i=1..n} Stirling2(n,i) * abs(Stirling1(i-1,k-1)), n >= 1, 1 <= k <= n.

1, 1, 1, 1, 4, 1, 1, 15, 9, 1, 1, 66, 66, 16, 1, 1, 365, 500, 190, 25, 1, 1, 2528, 4215, 2150, 435, 36, 1, 1, 21259, 40355, 25235, 6825, 861, 49, 1, 1, 210430, 438256, 317632, 105910, 17836, 1540, 64, 1, 1, 2393769, 5352534, 4338264, 1693734, 352926, 40656, 2556, 81, 1

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

Cf. A008275 (Stirling1), A008277 (Stirling2).

Sequence in context: A141724 A208956 A271705 * A343804 A157211 A176428

Adjacent sequences: A320277 A320278 A320279 * A320281 A320282 A320283

Keyword

nonn,tabl

Author

Michel Marcus, Oct 09 2018

Status

approved