A128065 Binomial transform of A128064.

1, 0, 2, -1, 2, 3, -2, 0, 6, 4, -3, -4, 6, 12, 5, -4, -10, 0, 20, 20, 6, -5, -18, -15, 20, 45, 30, 7, -6, -28, -42, 0, 70, 84, 42, 8, -7, -40, -84, -56, 70, 168, 140, 56, 9, -8, -54, -144, -168, 0, 252, 336, 216, 72, 10

Offset: 1

Author

Gary W. Adamson, Feb 14 2007

Keywords

• tabl
• sign

Comments

A128064 * A007318 = A103406 row sums = 2^(n-1).

Examples

			First few rows of the triangle are:
   1;
   0,  2;
  -1,  2,  3;
  -2,  0,  6,  4;
  -3, -4,  6, 12,  5;
  ...
		

Crossrefs

Cf. A128064, A103406.

Programs

Magma

/* As triangle */ [[(k+1)*(Binomial(n,k)-Binomial(n,k+1)): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jul 12 2019

Mathematica

Table[(k + 1) (Binomial[n, k] - Binomial[n, k + 1]), {n, 0,
12}, {k, 0, n}] // Flatten (* Nathaniel MacFadden, Jul 11 2019 *)

Formula

A007318 * A128064 as infinite lower triangular matrices.

Extensions

a(43) corrected by Nathaniel MacFadden, Jul 11 2019