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A177944 Array T(n,m) = 1/Beta(n+1, m+1) - n - m read by antidiagonals. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 11 23:43 EDT 2020. Contains 335653 sequences. (Running on oeis4.)