A368479
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} 2^j * j^k.
Original entry on oeis.org
1, 0, 3, 0, 2, 7, 0, 2, 10, 15, 0, 2, 18, 34, 31, 0, 2, 34, 90, 98, 63, 0, 2, 66, 250, 346, 258, 127, 0, 2, 130, 714, 1274, 1146, 642, 255, 0, 2, 258, 2074, 4810, 5274, 3450, 1538, 511, 0, 2, 514, 6090, 18458, 24810, 19098, 9722, 3586, 1023
Offset: 0
Square array begins:
1, 0, 0, 0, 0, 0, 0, ...
3, 2, 2, 2, 2, 2, 2, ...
7, 10, 18, 34, 66, 130, 258, ...
15, 34, 90, 250, 714, 2074, 6090, ...
31, 98, 346, 1274, 4810, 18458, 71626, ...
63, 258, 1146, 5274, 24810, 118458, 571626, ...
127, 642, 3450, 19098, 107754, 616122, 3557610, ...
A368487
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^j * binomial(j+k-1,j).
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 10, 17, 4, 1, 1, 17, 64, 49, 5, 1, 1, 26, 177, 334, 129, 6, 1, 1, 37, 401, 1457, 1549, 321, 7, 1, 1, 50, 793, 4776, 10417, 6652, 769, 8, 1, 1, 65, 1422, 12889, 48526, 67761, 27064, 1793, 9, 1, 1, 82, 2369, 30234, 176185, 442276, 411825, 105796, 4097, 10, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 5, 10, 17, 26, ...
1, 3, 17, 64, 177, 401, ...
1, 4, 49, 334, 1457, 4776, ...
1, 5, 129, 1549, 10417, 48526, ...
1, 6, 321, 6652, 67761, 442276, ...
-
T(n, k) = sum(j=0, n, k^j*binomial(j+k-1, j));
A368504
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^(n-j) * j^k.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 6, 1, 0, 1, 11, 21, 10, 1, 0, 1, 20, 60, 58, 15, 1, 0, 1, 37, 161, 244, 141, 21, 1, 0, 1, 70, 428, 900, 857, 318, 28, 1, 0, 1, 135, 1149, 3164, 4225, 2787, 685, 36, 1, 0, 1, 264, 3132, 10990, 18945, 18196, 8704, 1434, 45, 1
Offset: 0
Square array begins:
1, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 3, 6, 11, 20, 37, 70, ...
1, 6, 21, 60, 161, 428, 1149, ...
1, 10, 58, 244, 900, 3164, 10990, ...
1, 15, 141, 857, 4225, 18945, 81565, ...
1, 21, 318, 2787, 18196, 102501, 536046, ...
Showing 1-3 of 3 results.