A188587 1-Euler triangle.

1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 14, 30, 14, 1, 1, 33, 146, 146, 33, 1, 1, 72, 603, 1168, 603, 72, 1, 1, 151, 2241, 7687, 7687, 2241, 151, 1, 1, 310, 7780, 44194, 76870, 44194, 7780, 310, 1, 1, 629, 25820, 231236, 649514, 649514, 231236, 25820, 629, 1, 1, 1268, 83121, 1131504, 4866222, 7794168, 4866222, 1131504, 83121, 1268, 1

Offset

0,8

Comments

Formed with the same recurrence as the Euler triangle A008292 (adjusted for offset), but with the middle element of row n=2 set to 1.

Row sums are A188588. Second column is A188589.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = 0 if k < 0 or k > n.

T(n,k) = 1 if k=0 or k=n or n=2.

T(n,k)= (n-k+1)*T(n-1,k-1) + (k+1)*T(n-1,k), n > 2 and 1 <= k < n.

Example

Triangle begins
  1;
  1,   1;
  1,   1,     1;
  1,   5,     5,      1;
  1,  14,    30,     14,      1;
  1,  33,   146,    146,     33,      1;
  1,  72,   603,   1168,    603,     72,      1;
  1, 151,  2241,   7687,   7687,   2241,    151,     1;
  1, 310,  7780,  44194,  76870,  44194,   7780,   310,   1;
  1, 629, 25820, 231236, 649514, 649514, 231236, 25820, 629, 1;

Maple

A188587 := proc(n, k) if k < 0 or k > n then 0; elif k=0 or k= n or n=2 then 1; else (n-k+1)*procname(n-1, k-1)+(k+1)*procname(n-1, k) ; end if; end proc:
seq(seq(A188587(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Apr 13 2011

Crossrefs

Sequence in context: A046571 A172349 A144403 * A373434 A174119 A156696

Adjacent sequences: A188584 A188585 A188586 * A188588 A188589 A188590

Keyword

nonn,easy,tabl

Author

Paul Barry, Apr 04 2011

Status

approved