A273754
Number of binary heaps on [n] that give a heap when the first element is removed.
Original entry on oeis.org
1, 1, 1, 2, 3, 8, 18, 70, 180, 770, 2610, 14570, 54720, 330960, 1562814, 11946080, 57126780, 429542960, 2465050968, 22517159760
Offset: 1
There are 3 (min) heaps for n=4: 1234, 1243, 1324. When the first element is removed only 2 heaps remain: 234, 243. Thus a(4) = 2.
a(5) = 3: 12345, 12354, 12435.
a(6) = 8: 123456, 123465, 123546, 123564, 123645, 123654, 124356, 124365.
A379272
Number of binary min-heaps on n elements from the set {0,1} that give a max-heap when reversed.
Original entry on oeis.org
1, 2, 3, 4, 6, 8, 10, 14, 18, 22, 33, 40, 54, 74, 93, 116, 172, 204, 268, 378, 482, 584, 905, 1036, 1378, 1858, 2520, 3002, 4700, 5298, 7089, 9456, 12420, 15452, 24160, 26542, 36646, 47634, 64183, 75568, 126118, 135226, 188098, 244172, 329098, 383142, 626452, 689466, 980284, 1229296, 1691506
Offset: 0
a(5) = 8: 00000, 00001, 00011, 00101, 00111, 01011, 01111, 11111.
a(6) = 10: 000000, 000001, 000011, 000101, 000111, 001011, 001111, 010111, 011111, 111111. Min-heaps on 6 elements from the set {0,1} that do not give a max-heap when reversed are: 000010, 000100, 000110, 001001, 001101, 010110.
a(7) = 14: 0000000, 0000001, 0000011, 0000101, 0000111, 0001011, 0001111, 0010011, 0010111, 0011011, 0011111, 0101111, 0111111, 1111111.
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