A073135 Table by antidiagonals of T(n,k) = 2*n*T(n,k-1) - n^2*T(n,k-2) + T(n,k-4) starting with T(n,1) = 1.

1, 2, 1, 3, 4, 1, 4, 12, 6, 1, 6, 32, 27, 8, 1, 10, 81, 108, 48, 10, 1, 17, 200, 406, 256, 75, 12, 1, 28, 488, 1470, 1281, 500, 108, 14, 1, 45, 1184, 5193, 6160, 3126, 864, 147, 16, 1, 72, 2865, 18036, 28832, 18770, 6481, 1372, 192, 18, 1, 116, 6924, 61885, 132352

Offset

0,2

Links

Table of n, a(n) for n=0..58.

Formula

T(n, k) = (A073133(n, k+2) - A073134(n, k+2))/2.

T(n, k) = Sum_{j=0..floor((k-1)/4)} abs(A053122(k-3*j-1, j)*n^(k-4*j-1)).

Example

Rows start:
  1, 2,  3,   4,    6,   10,    17, ...;
  1, 4, 12,  32,   81,  200,   488, ...;
  1, 6, 27, 108,  406, 1470,  5193, ...;
  1, 8, 48, 256, 1281, 6160, 28832, ...;
  ...

Crossrefs

Cf. A053122, A073133, A073134.

Rows include A024490, A048776.

Columns include A000012, A005843, A033428, A033430.

Sequence in context: A240783 A327083 A104002 * A391485 A063804 A387934

Adjacent sequences: A073132 A073133 A073134 * A073136 A073137 A073138

Keyword

nonn,tabl

Author

Henry Bottomley, Jul 16 2002

Status

approved