This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A007501 M0818 #66 Jul 22 2025 00:28:35
%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_, Feb 01 2001
%C A007501 With a(0) = 2, a(n+1) is the number of possible distinct sums between any number of elements in {1,...,a(n)}. - _Derek Orr_, Dec 13 2014
%D A007501 W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. Rec. Math., 12 (1979), 104-111.
%D A007501 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007501 Reinhard Zumkeller, <a href="/A007501/b007501.txt">Table of n, a(n) for n = 0..12</a>
%H A007501 G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?number_id=2321">41041 (another Prime Pages' Curiosity)</a>
%H A007501 J. C. Kieffer, <a href="http://dx.doi.org/10.1109/CCP.2011.36">Hierarchical Type Classes and Their Entropy Functions</a>, in 2011 First International Conference on Data Compression, Communications and Processing, pp. 246-254; Digital Object Identifier: 10.1109/CCP.2011.36.
%H A007501 J. V. Post, <a href="http://web.archive.org/web/20191228140821id_/http://www.magicdragon.com/math.html">Math Pages</a> [wayback copy]
%H A007501 J.S. Seneschal, <a href="/A007501/a007501.jpg">Iteration of Complete Graphs</a>
%H A007501 Stephan Wagner, <a href="https://www.math.tugraz.at/~wagner/balanced.pdf">Enumeration of highly balanced trees</a>
%F A007501 a(n) = A006893(n+1) + 1.
%F A007501 a(n+1) = A000217(a(n)). - _Reinhard Zumkeller_, Aug 15 2013
%F A007501 a(n) ~ 2 * c^(2^n), where c = 1.34576817070125852633753712522207761954658547520962441996... . - _Vaclav Kotesovec_, Dec 17 2014
%F A007501 a(n) = A145272(n) + a(n-1). - _J.S. Seneschal_, Jul 17 2025
%e A007501 Example for depth 2 (the nonisomorphic possibilities 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)
%o A007501 (Haskell)
%o A007501 a007501 n = a007501_list !! n
%o A007501 a007501_list = iterate a000217 2 -- _Reinhard Zumkeller_, Aug 15 2013
%Y A007501 Cf. A000217, A006893.
%Y A007501 Cf. A117872 (parity), A275342 (2-adic valuation).
%Y A007501 Cf. A129440.
%Y A007501 Cf. A013589 (start=4), A050542 (start=5), A050548 (start=7), A050536 (start=8), A050909 (start=9).
%Y A007501 Cf. A108225, A145272.
%K A007501 nonn,easy
%O A007501 0,1
%A A007501 _N. J. A. Sloane_, _Robert G. Wilson v_