A127625 Triangle T(n,k) = binomial(n-1,k-1)*A001511(k), 1<=k<=n, read by rows.

1, 1, 2, 1, 4, 1, 1, 6, 3, 3, 1, 8, 6, 12, 1, 1, 10, 10, 30, 5, 2, 1, 12, 15, 60, 15, 12, 1, 1, 14, 21, 105, 35, 42, 7, 4, 1, 16, 28, 168, 70, 112, 28, 32, 1, 1, 18, 36, 252, 126, 252, 84, 144, 9, 2, 1, 20, 45, 360, 210, 504, 210, 480, 45, 20, 1

Offset

1,3

Comments

Column k of Pascal's triangle is multiplied by the k-th entry of the ruler sequence.

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Formula

T(n,n) = A001511(n).

Example

First few rows of the triangle are:
1;
1, 2;
1, 4, 1;
1, 6, 3, 3;
1, 8, 6, 12, 1;
1, 10, 10, 30, 5, 2;
1, 12, 15, 60, 15, 12, 1;
...

Mathematica

T[n_, k_]:=Binomial[n-1, k-1]*IntegerExponent[2k, 2]; Table[T[n, k], {n, 9}, {k, n}]//Flatten (* James C. McMahon, Jan 01 2025 *)

Crossrefs

Cf. A106461 (row sums), A001511.

Sequence in context: A191310 A124845 A191392 * A124844 A133934 A055327

Adjacent sequences: A127622 A127623 A127624 * A127626 A127627 A127628

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 20 2007

Extensions

a(46)-a(66) from James C. McMahon, Jan 01 2025

Status

approved