OFFSET
0,3
COMMENTS
FORMULA
EXAMPLE
T(7,3) = 66 = 1*4+8*3+14*2+10*1 = T(4,0)*4+T(4,1)*3+T(4,2)*2+T(4,3)*1; this is also the third term of the 4th-diagonal.
The 6th antidiagonal is {1,10,14,4}, which has a sum of 29 = A000990(6) = number of 2-line partitions of 6.
Rows begin:
{1},
{1,2},
{1,4,3},
{1,6,7,4},
{1,8,14,10,5},
{1,10,22,22,13,6},
{1,12,33,40,30,16,7},
{1,14,45,66,58,38,19,8},
{1,16,60,100,104,76,46,22,9},
{1,18,76,146,168,142,94,54,25,10},
{1,20,95,202,262,242,180,112,62,28,11},
{1,22,115,272,386,394,316,218,130,70,31,12},...
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(k==0, 1, sum(j=0, min(k, n-k), (k-j+1)*T(n-k, j))))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 14 2004
STATUS
approved