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 A321194 #11 Jan 12 2024 00:48:52
%S A321194 1,3,1,6,3,1,17,12,3,1,40,35,12,3,1,125,112,45,12,3,1,354,347,148,45,
%T A321194 12,3,1,1159,1122,512,163,45,12,3,1,3774,3651,1724,572,163,45,12,3,1,
%U A321194 13113,12320,5937,2020,593,163,45,12,3,1,46426,42407,20492,7117,2110,593,163,45,12,3,1
%N A321194 Regular triangle where T(n,k) is the number of non-isomorphic multiset partitions of weight n with k connected components.
%H A321194 Andrew Howroyd, <a href="/A321194/b321194.txt">Table of n, a(n) for n = 1..1275</a> (rows 1..50)
%F A321194 O.g.f.: Product 1/(1 - t*x^n)^A007718(n).
%e A321194 Triangle begins:
%e A321194 1
%e A321194 3 1
%e A321194 6 3 1
%e A321194 17 12 3 1
%e A321194 40 35 12 3 1
%e A321194 125 112 45 12 3 1
%e A321194 354 347 148 45 12 3 1
%e A321194 1159 1122 512 163 45 12 3 1
%e A321194 3774 3651 1724 572 163 45 12 3 1
%e A321194 13113 12320 5937 2020 593 163 45 12 3 1
%e A321194 The fourth row counts the following non-isomorphic multiset partitions.
%e A321194 {{1,1,1,1}} {{1,1},{2,2}} {{1},{2},{3,3}} {{1},{2},{3},{4}}
%e A321194 {{1,1,2,2}} {{1},{2,2,2}} {{1},{2},{3,4}}
%e A321194 {{1,2,2,2}} {{1},{2,3,3}} {{1},{2},{3},{3}}
%e A321194 {{1,2,3,3}} {{1,2},{3,3}}
%e A321194 {{1,2,3,4}} {{1},{2,3,4}}
%e A321194 {{1},{1,1,1}} {{1,2},{3,4}}
%e A321194 {{1,1},{1,1}} {{1},{1},{2,2}}
%e A321194 {{1},{1,2,2}} {{1},{1},{2,3}}
%e A321194 {{1,2},{1,2}} {{1},{2},{2,2}}
%e A321194 {{1,2},{2,2}} {{1},{3},{2,3}}
%e A321194 {{1,3},{2,3}} {{1},{1},{2},{2}}
%e A321194 {{2},{1,2,2}} {{1},{2},{2},{2}}
%e A321194 {{3},{1,2,3}}
%e A321194 {{1},{1},{1,1}}
%e A321194 {{1},{2},{1,2}}
%e A321194 {{2},{2},{1,2}}
%e A321194 {{1},{1},{1},{1}}
%Y A321194 First column is A007718. Row sums are A007716.
%Y A321194 Cf. A006126, A048143, A143543, A306005, A316983, A317672, A317674, A319616, A321155.
%K A321194 nonn,tabl
%O A321194 1,2
%A A321194 _Gus Wiseman_, Oct 29 2018
%E A321194 Terms a(56) and beyond from _Andrew Howroyd_, Jan 11 2024