A000615 - OEIS

%I M0379 N0142 N0747 #31 Oct 27 2023 03:22:39

%S 2,2,8,72,1536,86080,14487040,8274797440,17494930604032

%N Threshold functions of exactly n variables.

%D S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2. - Row 4.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence in two entries, N0142 and N0747).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Goto, Eiichi, and Hidetosi Takahasi, <a href="/A000371/a000371_1.pdf">Some Theorems Useful in Threshold Logic for Enumerating Boolean Functions</a>, in Proceedings International Federation for Information Processing (IFIP) Congress, 1962, pp. 747-752. [Annotated scans of certain pages]

%H Alastair D. King, <a href="/A002080/a002080.pdf">Comments on A002080 and related sequences based on threshold functions</a>, Mar 17 2023.

%H S. Muroga, I. Toda and M. Kondo, <a href="https://doi.org/10.1090/S0025-5718-62-99195-0">Majority decision functions of up to six variables</a>, Math. Comp., 16 (1962), 459-472.

%H S. Muroga, I. Toda and M. Kondo, <a href="/A001528/a001528.pdf">Majority decision functions of up to six variables</a>, Math. Comp., 16 (1962), 459-472. [Annotated partially scanned copy]

%H S. Muroga, T. Tsuboi and C. R. Baugh, <a href="https://doi.org/10.1109/T-C.1970.223046">Enumeration of threshold functions of eight variables</a>, IEEE Trans. Computers, 19 (1970), 818-825.

%H 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 <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%F A000609(n) = Sum_{k=0..n} a(k)*binomial(n,k). - Alastair D. King, Mar 17, 2023.

%Y Cf. A000609.

%K nonn,more

%O 0,1

%A _N. J. A. Sloane_

%E Entry revised by _N. J. A. Sloane_, Jun 11 2012