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 A380124 #22 Aug 24 2025 16:00:29
%S A380124 0,0,1,3,8,17,40,78,162,308,591,1068,1975,3445,6067,10366,17683,29375,
%T A380124 48886,79487,129220,206457,328782,516286,808903,1251135,1929061,
%U A380124 2944622,4478131,6749574,10139972,15110286,22440924,33099258,48645223,71056244,103449482,149757609
%N A380124 Total number of ways of partitioning n and any natural number less than n into the same number of parts.
%H A380124 Alois P. Heinz, <a href="/A380124/b380124.txt">Table of n, a(n) for n = 0..1000</a>
%F A380124 a(n) = Sum_{i=1..n-1} Sum_{j=1..i} p(n,j)*p(i,j), where p(n,j) is the number of partitions of n into j positive parts (A008284, A072233).
%e A380124 For example, a(4)=8:
%e A380124 4 and 1: (4,1),
%e A380124 4 and 2: (4,2) (3+1,1+1) (2+2,1+1),
%e A380124 4 and 3: (4,3) (3+1,2+1) (2+2,2+1) (2+1+1,1+1+1).
%Y A380124 Similar to A380125, A380126.
%Y A380124 Cf. A008284, A072233.
%K A380124 nonn,changed
%O A380124 0,4
%A A380124 _Aidan Markey_, Jan 12 2025
%E A380124 More terms from _Chai Wah Wu_, Feb 19 2025