A124732 Triangle P*M, where P is the Pascal triangle written as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,1,2,...) in the main diagonal and (2,1,2,1,...) in the subdiagonal.

1, 3, 2, 5, 5, 1, 7, 9, 5, 2, 9, 14, 14, 9, 1, 11, 20, 30, 25, 7, 2, 13, 27, 55, 55, 27, 13, 1, 15, 35, 91, 105, 77, 49, 9, 2, 17, 44, 140, 182, 182, 140, 44, 17, 1, 19, 54, 204, 294, 378, 336, 156, 81, 11, 2, 21, 65, 285, 450, 714, 714, 450, 285, 65, 21, 1, 23, 77, 385, 660

Offset

1,2

Comments

Row sums = A052940: (1, 5, 11, 23, 47, 95, ...).

Links

Table of n, a(n) for n=1..70.

Formula

T(n,k) = binomial(n,k)*(3n-(-1)^k*(n-2*k))/(2n) (1 <= k <= n).

Example

First 3 rows of the triangle are (1; 3,2; 5,5,1) since [1,0,0; 1,1,0; 1,2,1] * [1,0,0; 2,2,0; 0,1,1] = [1,0,0; 3,2,0; 5,5,1].
First few rows of the triangle are:
   1;
   3,   2;
   5,   5,   1;
   7,   9,   5,   2;
   9,  14,  14,   9,   1;
  11,  20,  30,  25,   7,   2;
  13,  27,  55,  55,  27,  13,   1;
  15,  35,  91, 105,  77,  49,   9,   2;
  ...

Maple

T:=(n, k)->binomial(n, k)*(3*n-(-1)^k*(n-2*k))/2/n: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form

Crossrefs

Cf. A124730, A052940.

Sequence in context: A095006 A159587 A369992 * A167552 A094787 A132778

Adjacent sequences: A124729 A124730 A124731 * A124733 A124734 A124735

Keyword

nonn,tabl

Author

Gary W. Adamson & Roger L. Bagula, Nov 05 2006

Extensions

Edited by N. J. A. Sloane, Nov 24 2006

Status

approved