A177944 Array T(n,m) = 1/Beta(n+1, m+1) - n - m read by antidiagonals.

1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 26, 16, 1, 1, 25, 55, 55, 25, 1, 1, 36, 99, 134, 99, 36, 1, 1, 49, 161, 273, 273, 161, 49, 1, 1, 64, 244, 496, 622, 496, 244, 64, 1, 1, 81, 351, 831, 1251, 1251, 831, 351, 81, 1

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.

Links

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

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

Sequence in context: A152237 A176282 A082043 * A174006 A124216 A008459

Adjacent sequences: A177941 A177942 A177943 * A177945 A177946 A177947

Keyword

nonn,easy,tabl

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