A397422 Triangle read by rows: T(n, k) = binomial(n+k, n) * |Stirling1(n, k)| * n^k.

1, 0, 2, 0, 6, 24, 0, 24, 270, 540, 0, 120, 2640, 13440, 17920, 0, 720, 26250, 245000, 787500, 787500, 0, 5040, 276192, 4082400, 23133600, 53887680, 43110144, 0, 40320, 3111696, 66843840, 582362550, 2329450200, 4239599364, 2826399576

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).

Example

Triangle begins:
  [0]  1;
  [1]  0,     2;
  [2]  0,     6,      24;
  [3]  0,    24,     270,      540;
  [4]  0,   120,    2640,    13440,     17920;
  [5]  0,   720,   26250,   245000,    787500,     787500;
  [6]  0,  5040,  276192,  4082400,  23133600,   53887680,   43110144;
  [7]  0, 40320, 3111696, 66843840, 582362550, 2329450200, 4239599364, 2826399576;

Maple

T := (n, k) -> abs(Stirling1(n, k))*binomial(n + k, n)*n^k:
seq(seq(T(n, k), k = 0..n), n = 0..7);

Mathematica

A397422[n_, k_] := If[k == 0, Boole[n == 0], Binomial[n + k, n]*Abs[StirlingS1[n, k]]*n^k];
Table[A397422[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jun 24 2026 *)

Crossrefs

Cf. A132393, A397400, A397324, A397421.

Sequence in context: A247443 A362685 A397421 * A171734 A278746 A391157

Adjacent sequences: A397418 A397420 A397421 * A397423 A397424 A397425

Keyword

nonn,tabl

Author

Peter Luschny, Jun 24 2026

Status

approved