A366159 Triangle read by rows: T(n, k) = Sum_{i=0..k-2} (-1)^(i+2) * (k-i-1)^n * binomial(k,i).

1, 1, 5, 1, 13, 23, 1, 29, 121, 119, 1, 61, 479, 1081, 719, 1, 125, 1681, 6719, 10081, 5039, 1, 253, 5543, 35281, 90719, 100801, 40319, 1, 509, 17641, 168839, 665281, 1239839, 1088641, 362879, 1, 1021, 54959, 763561, 4339439, 12096001, 17539199, 12700801, 3628799

Offset

2,3

Links

Michael De Vlieger, Table of n, a(n) for n = 2..11176 (rows 2..150, flattened)

Dmitry N. Kozlov, Stirling complexes, arXiv:2309.17142 [math.CO], 2023.

Example

Triangle begins:
  1;
  1,    5;
  1,   13,    23;
  1,   29,   121,    119;
  1,   61,   479,   1081,     719;
  1,  125,  1681,   6719,   10081,     5039;
  1,  253,  5543,  35281,   90719,   100801,    40319;
  1,  509, 17641, 168839,  665281,  1239839,  1088641,   362879;
  1, 1021, 54959, 763561, 4339439, 12096001, 17539199, 12700801, 3628799;
  ...

Mathematica

Table[Sum[(-1)^(i + 2)*(k - i - 1)^n*Binomial[k, i], {i, 0, k - 2} ], {n, 2, 10}, {k, 2, n}] // Flatten (* Michael De Vlieger, Oct 02 2023 *)

Prog

(PARI) T(n, k) = sum(i=0, k-2, (-1)^(i+2) * (k-i-1)^n * binomial(k, i));
tabl(nn) = for (n=2, nn, for (k=2, n, print1(T(n, k), ", ")));

Crossrefs

Cf. A000012 (col 2), A036563 (col 3), A033312 (right border).

Cf. A105060.

Sequence in context: A205961 A146620 A300291 * A174504 A270654 A067558

Adjacent sequences: A366156 A366157 A366158 * A366160 A366161 A366162

Keyword

nonn,tabl

Author

Michel Marcus, Oct 02 2023

Status

approved