A361835
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*k,k) * binomial(n*k,n-k).
Original entry on oeis.org
1, 2, 2, -10, -10, 242, -678, -7054, 88342, -207646, -6015904, 88310862, -312514816, -8847633338, 184252541514, -1269592841970, -17662739133178, 634109114537218, -7914500471718552, -18165019012117450, 2936604063787679650, -62899139815867627378
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(2*k, k)*binomial(n*k, n-k));
A361830
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(2*j,j) * binomial(k*j,n-j).
Original entry on oeis.org
1, 1, 2, 1, 2, 6, 1, 2, 8, 20, 1, 2, 10, 32, 70, 1, 2, 12, 46, 136, 252, 1, 2, 14, 62, 226, 592, 924, 1, 2, 16, 80, 342, 1136, 2624, 3432, 1, 2, 18, 100, 486, 1932, 5810, 11776, 12870, 1, 2, 20, 122, 660, 3030, 11094, 30080, 53344, 48620
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, ...
6, 8, 10, 12, 14, 16, ...
20, 32, 46, 62, 80, 100, ...
70, 136, 226, 342, 486, 660, ...
252, 592, 1136, 1932, 3030, 4482, ...
-
T(n, k) = sum(j=0, n, binomial(2*j, j)*binomial(k*j, n-j));
A361846
a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n*k,n-k).
Original entry on oeis.org
1, 3, 24, 243, 2973, 41676, 652662, 11228556, 209674050, 4211011422, 90309000630, 2056139084544, 49460437075896, 1251936022103679, 33228751234896060, 922028391785300940, 26676362307801924057, 802875670635086298600
Offset: 0
-
a(n) = sum(k=0, n, (-9)^k*binomial(-1/3, k)*binomial(n*k, n-k));
Showing 1-3 of 3 results.