A199479 Triangle T(n,k), read by rows, given by (1,0,0,0,0,0,0,0,0,0,...) DELTA (1,1,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.

1, 1, 1, 1, 3, 2, 1, 5, 9, 5, 1, 7, 20, 27, 13, 1, 9, 35, 73, 80, 34, 1, 11, 54, 151, 252, 234, 89, 1, 13, 77, 269, 597, 837, 677, 233, 1, 15, 104, 435, 1199, 2225, 2702, 1941, 610, 1, 17, 135, 657, 2158, 4956, 7943, 8533, 5523, 1597

Offset

0,5

Comments

Mirror image of triangle in A147703.

Links

Table of n, a(n) for n=0..54.

Formula

Sum_{k=0..n} T(n,k)*x^k = A152620(n), A152594(n), A000007(n), A000012(n), A006012(n), A152596(n), A152599(n) for x=-3,-2,-1,0,1,2,3 respectively.

T(n,n) = A001519(n).

G.f.: (1-2y*x)/(1-(1+3y)*x+y*(1+y)*x^2).

Example

Triangle begins:
  1;
  1,  1;
  1,  3,  2;
  1,  5,  9,  5;
  1,  7, 20, 27, 13;
  1,  9, 35, 73, 80, 34;

Crossrefs

Cf. A001519, A059502, A000012, A005408, A014107.

Sequence in context: A077976 A021912 A114597 * A050165 A330784 A198876

Adjacent sequences: A199476 A199477 A199478 * A199480 A199481 A199482

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Nov 06 2011

Status

approved