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 A124426 #15 Sep 08 2022 08:45:28
%S A124426 1,2,10,75,780,10556,178031,3630780,87548580,2452523325,78697155750,
%T A124426 2859220516290,116482516809889,5277304280371714,264005848594606490,
%U A124426 14493602135008296115,868435614538568029188,56520205738693680322836
%N A124426 Product of two successive Bell numbers.
%C A124426 Number of partitions of the set {1,2,...,2n+1} having no blocks that contain both odd and even entries. Example: a(2)=10 because we have 135|24, 15|24|3, 1|24|35, 135|2|4, 15|2|3|4, 1|2|35|4, 13|24|5, 1|24|3|5, 13|2|4|5 and 1|2|3|4|5. a(n)=A124419(2n+1)=A124418(2n+1,0).
%H A124426 Harvey P. Dale, <a href="/A124426/b124426.txt">Table of n, a(n) for n = 0..324</a>
%F A124426 a(n) = B(n)*B(n+1), where B(q) are the Bell numbers (A000110), i.e., B(n) = Sum_{k=1..n} S2(n,k), S2(n,k) being the Stirling numbers of the 2nd kind (A008277).
%p A124426 with(combinat): seq(bell(n)*bell(n+1),n=0..19);
%t A124426 Times@@@Partition[BellB[Range[0,20]],2,1] (* _Harvey P. Dale_, Oct 07 2018 *)
%o A124426 (Magma) [&*[ Bell(n+k): k in [0..1] ]: n in [0..30]]; // _Vincenzo Librandi_, Apr 09 2020
%Y A124426 Cf. A000110, A008277, A124418, A124419.
%K A124426 nonn
%O A124426 0,2
%A A124426 _Emeric Deutsch_ and _Paul D. Hanna_, Nov 03 2006