%I A007501 M0818
%S A007501 2,3,6,21,231,26796,359026206,64449908476890321,
%T A007501 2076895351339769460477611370186681,
%U A007501 2156747150208372213435450937462082366919951682912789656986079991221
%N A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
%C A007501 Number of nonisomorphic complete binary trees with leaves colored using 
               two colors - Brendan McKay (bdm(AT)cs.anu.edu.au), Feb 01, 2001
%C A007501 Let {t(k)} be the triangular numbers (A000219). Then a(0) = 2; for n>
               0, a(n) = t(a(n-1)). - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Nov 13 2004
%D A007501 W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. 
               Rec. Math., 12 (1979), 104-111.
%D A007501 J. V. Post, "Iterated Triangular Numbers", preprint.
%D A007501 J. V. Post, "Iterated Polygonal Numbers", preprint.
%D A007501 J. V. Post, "Triangular Carmichael Numbers: The First 22 Identified", 
               preprint.
%D A007501 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007501 G. L. Honaker, Jr., <a href="http://primes.utm.edu/curios/page.php?number_id=2321">
               41041 (another Prime Pages' Curiosity)</a>
%H A007501 J. V. Post, <a href="http://www.magicdragon.com/math.html">Math Pages</
               a>
%e A007501 Example for depth 2 (the nonisomorpic possibilites are AAAA, AAAB, AABB, 
               ABAB, ABBB, BBBB):
%e A007501 .........o
%e A007501 ......../.\
%e A007501 ......./...\
%e A007501 ......o.....o
%e A007501 ...../.\.../.\
%e A007501 ..../...\./...\
%e A007501 ....A...B.B...B
%t A007501 f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
%o A007501 (PARI) a(n)=if(n<1,2,a(n-1)*(1+a(n-1))/2)
%Y A007501 Equals A006893(n+1) + 1. Cf. A000217.
%Y A007501 Cf. A129440.
%Y A007501 Sequence in context: A012924 A024485 A013155 this_sequence A015773 A015768 
               A094470
%Y A007501 Adjacent sequences: A007498 A007499 A007500 this_sequence A007502 A007503 
               A007504
%K A007501 nonn,easy
%O A007501 0,1
%A A007501 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)