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

1,11

Links

Table of n, a(n) for n=1..91.

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

Formula

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

Example

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,
  ...

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 *)

Prog

(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);

Crossrefs

Cf. A007814, A008275.

Sequence in context: A060096 A245756 A360672 * A152892 A193002 A366725

Adjacent sequences: A322509 A322510 A322511 * A322513 A322514 A322515

Keyword

nonn,tabl

Author

Michel Marcus, Dec 13 2018

Status

approved