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 A050315 #25 May 21 2021 08:11:19
%S A050315 1,1,1,2,1,2,2,5,1,2,2,5,2,5,5,15,1,2,2,5,2,5,5,15,2,5,5,15,5,15,15,
%T A050315 52,1,2,2,5,2,5,5,15,2,5,5,15,5,15,15,52,2,5,5,15,5,15,15,52,5,15,15,
%U A050315 52,15,52,52,203,1,2,2,5,2,5,5,15,2,5,5,15,5,15,15,52,2,5,5,15,5,15
%N A050315 Main diagonal of A050314.
%C A050315 Also, a(n) is the number of odd multinomial coefficients n!/(k_1!...k_m!) with 1 <= k_1 <= ... <= k_m and k_1 + ... + k_m = n. - _Pontus von Brömssen_, Mar 23 2018
%C A050315 From _Gus Wiseman_, Mar 30 2019: (Start)
%C A050315 Also the number of strict integer partitions of n with no binary carries. The Heinz numbers of these partitions are given by A325100. A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion. For example, the a(1) = 1 through a(15) = 15 strict integer partitions with no binary carries are:
%C A050315 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C) (D) (E) (F)
%C A050315 (21) (41) (42) (43) (81) (82) (83) (84) (85) (86) (87)
%C A050315 (52) (92) (94) (A4) (96)
%C A050315 (61) (A1) (C1) (C2) (A5)
%C A050315 (421) (821) (841) (842) (B4)
%C A050315 (C3)
%C A050315 (D2)
%C A050315 (E1)
%C A050315 (843)
%C A050315 (852)
%C A050315 (861)
%C A050315 (942)
%C A050315 (A41)
%C A050315 (C21)
%C A050315 (8421)
%C A050315 (End)
%H A050315 Alois P. Heinz, <a href="/A050315/b050315.txt">Table of n, a(n) for n = 0..16383</a>
%H A050315 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%F A050315 Bell number of number of 1's in binary: a(n) = A000110(A000120(n)).
%p A050315 a:= n-> combinat[bell](add(i,i=convert(n, base, 2))):
%p A050315 seq(a(n), n=0..100); # _Alois P. Heinz_, Apr 08 2019
%t A050315 binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A050315 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A050315 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&stableQ[#,Intersection[binpos[#1],binpos[#2]]!={}&]&]],{n,0,20}] (* _Gus Wiseman_, Mar 30 2019 *)
%t A050315 a[n_] := BellB[DigitCount[n, 2, 1]];
%t A050315 a /@ Range[0, 100] (* _Jean-François Alcover_, May 21 2021 *)
%Y A050315 Cf. A000110, A000120, A050314.
%Y A050315 Cf. A070939, A080572, A247935, A267610.
%Y A050315 Cf. A325093, A325095, A325096, A325099, A325100, A325103, A325110, A325123.
%Y A050315 Main diagonal of A307431 and of A307505.
%K A050315 nonn
%O A050315 0,4
%A A050315 _Christian G. Bower_, Sep 15 1999