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 A119271 #30 Jan 20 2025 03:54:36 %S A119271 1,0,1,0,1,1,0,1,3,1,0,1,5,6,1,0,1,9,18,10,1,0,1,13,44,49,15,1,0,1,20, %T A119271 97,172,110,21,1,0,1,28,195,512,550,216,28,1,0,1,40,377,1370,2195, %U A119271 1486,385,36,1,0,1,54,694,3396,7603,7886,3514,638,45,1,0,1,75,1251,7968 %N A119271 Triangle: number of exactly (m-1)-dimensional partitions of n, for n >= 1, m >= 0. %C A119271 The partition of 1 is considered to be dimension -1 by convention. %H A119271 Suresh Govindarajan, <a href="/A119271/b119271.txt">Rows n = 1..26 of Triangle</a> %H A119271 Suresh Govindarajan, <a href="http://www.physics.iitm.ac.in/~suresh/partitions.html">Partitions Generator</a> (gives partitions of integers <= 25 in any dimension using this triangle). %H A119271 Suresh Govindarajan, <a href="http://boltzmann.wikidot.com/refined-counting">Refined counting of higher-dimensional partitions</a> %H A119271 Suresh Govindarajan, <a href="http://arxiv.org/abs/1203.4419">Notes on higher-dimensional partitions</a>, arXiv preprint arXiv:1203.4419 [math.CO], 2012. %F A119271 a(n,m) = A096806(n,m-1)-a(n,m-1). Binomial transform of n-th row lists the (m-1) dimensional partitions of n. %e A119271 Table starts: %e A119271 1, %e A119271 0,1, %e A119271 0,1,1, %e A119271 0,1,3,1, %e A119271 0,1,5,6,1, %e A119271 ... %Y A119271 Cf. A119270, A096806. Column 1 is A007042. %K A119271 nonn,tabl,hard %O A119271 1,9 %A A119271 _Franklin T. Adams-Watters_, May 11 2006