A273754 - OEIS

%I #13 May 29 2016 17:02:00

%S 1,1,1,2,3,8,18,70,180,770,2610,14570,54720,330960,1562814,11946080,

%T 57126780,429542960,2465050968,22517159760

%N Number of binary heaps on [n] that give a heap when the first element is removed.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Heap.html">Heap</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_heap">Binary heap</a>

%e 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.

%e a(5) = 3: 12345, 12354, 12435.

%e a(6) = 8: 123456, 123465, 123546, 123564, 123645, 123654, 124356, 124365.

%Y Cf. A056971, A273755.

%K nonn,more

%O 1,4

%A _Alois P. Heinz_, May 29 2016