A394442 Triangle read by rows: T(n, k) = Sum_{j=0..k} 2^(n - j) * j! * Stirling2(n, j).

1, 0, 1, 0, 2, 4, 0, 4, 16, 22, 0, 8, 64, 136, 160, 0, 16, 256, 856, 1336, 1456, 0, 32, 1024, 5344, 11584, 15184, 15904, 0, 64, 4096, 32992, 100192, 167392, 197632, 202672, 0, 128, 16384, 201856, 855040, 1863040, 2629120, 2911360, 2951680

Offset

0,5

Links

Table of n, a(n) for n=0..44.

Example

Triangle starts:
  [0]  1;
  [1]  0,  1;
  [2]  0,  2,    4;
  [3]  0,  4,   16,    22;
  [4]  0,  8,   64,   136,    160;
  [5]  0, 16,  256,   856,   1336,   1456;
  [6]  0, 32, 1024,  5344,  11584,  15184,  15904;
  [7]  0, 64, 4096, 32992, 100192, 167392, 197632, 202672;

Maple

T := (n, k) -> local j; add(2^(n - j) * j! * Stirling2(n, j), j = 0..k):
seq(seq(T(n, k), k = 0..n), n = 0..8);

Mathematica

T[n_, k_]:=Sum[2^(n-j)*j!*StirlingS2[n, j], {j, 0, k}]; Table[T[n, k], {n, 0, 8}, {k, 0, n}]//Flatten (* James C. McMahon, Mar 27 2026 *)

Crossrefs

Cf. A131689, A048993, A122704, A123125, A394440 (row sums).

Sequence in context: A256487 A079985 A059226 * A221655 A221087 A387485

Adjacent sequences: A394439 A394440 A394441 * A394443 A394444 A394445

Keyword

nonn,tabl

Author

Peter Luschny, Mar 20 2026

Status

approved