A362789
Triangle read by rows. T(n, k) = FallingFactorial(n - k, k) * Stirling2(n - k, k), for n >= 0 and 0 <= k <= n//2, where '//' denotes integer division.
Original entry on oeis.org
1, 0, 0, 1, 0, 2, 0, 3, 2, 0, 4, 18, 0, 5, 84, 6, 0, 6, 300, 144, 0, 7, 930, 1500, 24, 0, 8, 2646, 10800, 1200, 0, 9, 7112, 63210, 23400, 120, 0, 10, 18360, 324576, 294000, 10800, 0, 11, 45990, 1524600, 2857680, 352800, 720, 0, 12, 112530, 6717600, 23496480, 7056000, 105840
Offset: 0
Triangle T(n, k) starts:
[0] 1;
[1] 0;
[2] 0, 1;
[3] 0, 2;
[4] 0, 3, 2;
[5] 0, 4, 18;
[6] 0, 5, 84, 6;
[7] 0, 6, 300, 144;
[8] 0, 7, 930, 1500, 24;
[9] 0, 8, 2646, 10800, 1200;
-
fallingFactorial := (x, n) -> (-1)^n * pochhammer(-x, n):
T := (n, k) -> fallingFactorial(n - k, k) * Stirling2(n - k, k):
seq(seq(T(n, k), k = 0..iquo(n,2)), n = 0..12);
-
def A362789(n, k):
return falling_factorial(n - k, k) * stirling_number2(n - k, k)
for n in range(10):
print([A362789(n, k) for k in range(n//2 + 1)])
A386936
Numbers that can be represented using their digits in the order of appearance, the operations +, -, *, /, ^, and any parentheses.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 9, 343, 736, 1285, 2187, 2592, 2737, 3125, 3685, 3972, 4096, 6455, 11664, 14641, 15552, 15585, 15617, 15618, 15622, 15624, 15626, 15632, 15645, 15655, 15656, 15662, 15667, 15698, 16377, 16384, 17536, 19683, 23328, 24576, 27639
Offset: 1
343 = (3+4)^3.
2737 = (2*7)^3-7.
46688 = (4 + 6^6/8)*8.
A365583
Numbers k with property that k can be represented by the digits present in k using the operations specified in the comment, and requiring fewer digits than the number of digits in k.
Original entry on oeis.org
1024, 1253, 1287, 1296, 1331, 2048, 2163, 2187, 2435, 2500, 2564, 2568, 2916, 3025, 3125, 3216, 3375, 3437, 3645, 3729, 4088, 4096, 4256, 4375, 4625, 5129, 5243, 6250, 6254, 7128, 7293, 7343, 7776, 8256, 9025, 9216, 9375, 9512, 10003, 10004
Offset: 1
For k = 3125, k can be represented as 5^5, using only 2 digits, which is less than the length of k, 4.
For k = 3437, k can be represented as (7^3)||7, using only 3 digits which is less than the length of k, 4.
For k = 10003, k can be represented as ((1||0)^3)||3, using only 4 digits, which is less than the length of k, 5.
Showing 1-3 of 3 results.
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