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 A002078 M0816 N0308 #48 Jun 28 2025 17:45:28
%S A002078 2,3,6,20,150,3287,244158,66291591,68863243522
%N A002078 N-equivalence classes of threshold functions of n or fewer variables.
%C A002078 It appears that this is the BinomialMean transform of A000609. (See A075271 for the definition of the transform.) - _John W. Layman_, Feb 21 2003. [This is now confirmed by the formulas below. - Alastair D. King, Mar 17 2023.]
%D A002078 S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 7.
%D A002078 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002078 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002078 Alastair D. King, <a href="/A002080/a002080.pdf">Comments on A002080 and related sequences based on threshold functions</a>, Mar 17 2023.
%H A002078 S. Muroga, <a href="/A000371/a000371.pdf">Threshold Logic and Its Applications</a>, Wiley, NY, 1971. [Annotated scans of a few pages]
%H A002078 Saburo Muroga, Iwao Toda, and Satoru Takasu, <a href="/A002079/a002079.pdf">Theory of majority decision elements</a>, Journal of the Franklin Institute 271.5 (1961): 376-418. [Annotated scans of pages 413 and 414 only]
%H A002078 S. Muroga, T. Tsuboi and C. R. Baugh, <a href="http://dx.doi.org/10.1109/T-C.1970.223046">Enumeration of threshold functions of eight variables</a>, IEEE Trans. Computers, 19 (1970), 818-825.
%H A002078 S. Muroga, T. Tsuboi and C. R. Baugh, <a href="/A002077/a002077.pdf">Enumeration of threshold functions of eight variables</a>, IEEE Trans. Computers, 19 (1970), 818-825. [Annotated scanned copy]
%H A002078 Michael Z. Spivey and Laura L. Steil, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Spivey/spivey7.html">The k-Binomial Transforms and the Hankel Transform</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
%H A002078 Eda Uyanık, Olivier Sobrie, Vincent Mousseau, Marc Pirlot, <a href="https://dx.doi.org/10.1016/j.dam.2017.04.010">Enumerating and categorizing positive Boolean functions separable by a k-additive capacity</a>, Discrete Applied Mathematics, Vol. 229, 1 October 2017, p. 17-30. See Table 4.
%H A002078 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>
%F A002078 a(n) = Sum_{k=0..n} A002079(k)*binomial(n,k) = (1/2^n)*Sum_{k=0..n} A000609(k)*binomial(n,k). - Alastair D. King, Mar 17 2023
%Y A002078 Cf. A000609, A002077, A002079, A002080, A075271.
%K A002078 nonn,more
%O A002078 0,1
%A A002078 _N. J. A. Sloane_