A124844 Triangle T(n,k)=binomial(n,k)*A061084(k), 0<=k<=n, read by rows.

1, 1, 2, 1, 4, -1, 1, 6, -3, 3, 1, 8, -6, 12, -4, 1, 10, -10, 30, -20, 7, 1, 12, -15, 60, -60, 42, -11, 1, 14, -21, 105, -140, 147, -77, 18, 1, 16, -28, 168, -280, 392, -308, 144, -29, 1, 18, -36, 252, -504, 882, -924, 648, -261, 47, 1, 20, -45, 360, -840, 1764, -2310, 2160, -1305, 470, -76

Offset: 0

Author

Gary W. Adamson, Nov 10 2006

Keywords

• sign
• easy
• tabl

Examples

			First few rows of the triangle are:
1;
1, 2;
1, 4, -1;
1, 6, -3, 3;
1, 8, -6, 12, -4;
1, 10, -10, 30, -20, 7;
1, 12, -15, 60, -60, 42, -11;
1, 14, -21, 105, -140, 147, -77, 18;
...
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Crossrefs

Cf. A061084, A000032, A000204 (row sums).

Cf. A007318.

Programs

Haskell

import Data.List (inits)
a124844 n k = a124844_tabl !! n !! k
a124844_row n = a124844_tabl !! n
a124844_tabl = zipWith (zipWith (*))
                       a007318_tabl $ tail $ inits a061084_list
-- Reinhard Zumkeller, Sep 15 2015

Formula

We let A061084 = the diagonal of an infinite matrix, M. Perform P*M and extract the zeros, where P = Pascal's triangle as an infinite lower triangular matrix.