A127967 A right-skewed Pascal triangle, with interspersed 1's on main diagonal.

1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 0, 4, 0, 3, 1, 1, 0, 5, 0, 6, 0, 1, 1, 0, 6, 0, 10, 0, 4, 1, 1, 0, 7, 0, 15, 0, 10, 0, 1, 1, 0, 8, 0, 21, 0, 20, 0, 5, 1, 1, 0, 9, 0, 28, 0, 35, 0, 15, 0, 1, 1, 0, 10, 0, 36, 0, 56, 0, 35, 0, 6, 1

Offset

0,9

Comments

Linked to Fibonacci numbers by row sums A127968. Inverse A127969 is linked to Genocchi numbers by its first column.

Links

Table of n, a(n) for n=0..77.

Formula

Column k is generated by x^(-2)*(x*(1-x)^(-1/2))^(k+2), where non-integer values are set to 0; or, column k has g.f. x^k/(1-x)^(1+k/2) if k is even, x^k if k is odd.

Example

Triangle begins
  1;
  1, 1;
  1, 0,  1;
  1, 0,  2, 1;
  1, 0,  3, 0,  1;
  1, 0,  4, 0,  3, 1;
  1, 0,  5, 0,  6, 0,  1;
  1, 0,  6, 0, 10, 0,  4, 1;
  1, 0,  7, 0, 15, 0, 10, 0,  1;
  1, 0,  8, 0, 21, 0, 20, 0,  5, 1;
  1, 0,  9, 0, 28, 0, 35, 0, 15, 0,  1;
  1, 0, 10, 0, 36, 0, 56, 0, 35, 0,  6, 1;
  1, 0, 11, 0, 45, 0, 84, 0, 70, 0, 21, 0, 1;

Crossrefs

Cf. A127968, A127969.

Sequence in context: A180984 A051628 A163540 * A147602 A114206 A073202

Adjacent sequences: A127964 A127965 A127966 * A127968 A127969 A127970

Keyword

easy,nonn,tabl

Author

Paul Barry, Feb 09 2007

Status

approved