A322512 Triangle read by rows of the 2-adic valuation (A007814) of Stirling numbers of first kind (A008275).

0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 0, 0, 0, 4, 2, 3, 0, 0, 0, 0, 4, 2, 2, 0, 3, 1, 2, 0, 7, 4, 2, 2, 0, 3, 1, 2, 0, 7, 4, 2, 5, 0, 0, 1, 1, 0, 0, 8, 5, 3, 2, 1, 0, 0, 1, 3, 0, 0, 8, 5, 3, 2, 1, 0, 1, 0, 1, 0, 1, 0, 10, 7, 7, 3, 2, 1, 0, 1, 0, 1, 0, 1, 0

Offset: 1

Author

Michel Marcus, Dec 13 2018

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  0,
  0, 0,
  1, 0, 0,
  1, 0, 1, 0,
  3, 1, 0, 1, 0,
  3, 1, 0, 0, 0, 0,
  4, 2, 3, 0, 0, 0, 0,
  4, 2, 2, 0, 3, 1, 2, 0,
  ...
		

Links

• Min Qiu, Shaofang Hong, The 2-adic valuations of Stirling numbers of the first kind, arXiv:1812.04539 [math.NT], 2018.

Crossrefs

Cf. A007814, A008275.

Programs

Mathematica

T[n_, k_] := IntegerExponent[StirlingS1[n, k], 2]; Table[T[n, k], {n, 1, 20}, {k, 1, n}] // Flatten (* Amiram Eldar, Dec 13 2018 *)

PARI

T(n,k) = valuation(stirling(n, k, 1), 2);
row(n) = vector(n, k, T(n,k));
tabl(nn) = vector(nn, k, row(k));(PARI) T(n,k) = valuation(stirling(n, k, 1), 2);

Formula

T(n,k) = A007814(A008275(n,k)).