A106461 -id:A106461 - cp's OEIS frontend

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

Gary W. Adamson, Jan 20 2007

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

			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;
...

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

Cf. A106461 (row sums), A001511.

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 *)

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

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

A129262 Triangle read by rows, A007318 * A115361.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 5, 4, 3, 1, 9, 8, 6, 4, 1, 16, 15, 11, 10, 5, 1, 27, 26, 21, 20, 15, 6, 1, 44, 43, 42, 36, 35, 21, 7, 1, 73, 72, 84, 64, 70, 56, 28, 8, 1, 130, 129, 162, 120, 127, 126, 84, 36, 9, 1, 251, 250, 297, 240, 220, 252, 210, 120, 45, 10, 1, 507, 506, 518, 495, 385, 463, 462, 330, 165, 55, 11, 1

Offset: 1

Gary W. Adamson, Apr 06 2007

Row sums give A106461.
Left column is A119968.
A128807 = A115361 * A007318.

			First few rows of the triangle:
  1;
  2,  1;
  3,  2,  1;
  5,  4,  3,  1;
  9,  8,  6,  4,  1;
 16, 15, 11, 10,  5,  1;
 27, 26, 21, 20, 15,  6,  1;
 44, 43, 42, 36, 35, 21,  7,  1;
  ...

Cf. A007318, A115361, A106461, A119968, A128807.

Binomial transform of A115361.

Terms a(23) and following corrected by Georg Fischer, Jul 04 2023

cp's OEIS Frontend

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

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