OFFSET
0,5
COMMENTS
Antidiagonal sums are 1, 2, 6, 20, 60, 162, 406, 968, 2232, 5030, ... = (d+1)*(2^d-d).
The values appear to be related to binomial(n,m)^2.
FORMULA
T(n,m) = Gamma(n+m+2)/(Gamma(n+1)*Gamma(m+1)) - n - m = T(m,n).
EXAMPLE
The array starts in row n=0, column m=0 as:
1,....1,....1,....1,.....1,.....1,.....1,.....1,
1,....4,....9,...16,....25,....36,....49,....64, A000290
1,....9,...26,...55,....99,...161,...244,...351, A154560
1,...16,...55,..134,...273,...496,...831,..1310,
1,...25,...99,..273,...622,..1251,..2300,..3949,
1,...36,..161,..496,..1251,..2762,..5533,.10284,
1,...49,..244,..831,..2300,..5533,.12000,.24011,
1,...64,..351,.1310,..3949,.10284,.24011,.51466,
MATHEMATICA
Clear[t, n];
t[n_, m_] = 1/Beta[n + 1, m + 1] - n - m;
a = Table[Table[t[n, m], {m, 0, 10}], {n, 0, 10}];
Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
Flatten[%]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, May 15 2010
EXTENSIONS
Examples written in natural order, closed formula for antidiag. sum - The Assoc. Eds. of the OEIS, Nov 03 2010
STATUS
approved