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 A005616 M1983 #49 Apr 03 2025 23:05:02 %S A005616 2,2,10,114,2154,56946,1935210,80371122,3944568042,223374129138, %T A005616 14335569726570,1028242536825906,81514988432370666, %U A005616 7077578056972377714,667946328512863533930,68080118128074301929138,7453010693997492901047018 %N A005616 Number of non-degenerate disjunctively-realizable functions of n variables. %C A005616 Number of non-degenerate fanout-free Boolean functions of n variables using And, Or, Xor, and Not gates. %D A005616 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005616 Andrew Howroyd, <a href="/A005616/b005616.txt">Table of n, a(n) for n = 0..200</a> %H A005616 E. A. Bender and J. T. Butler, <a href="/A005612/a005612.pdf">Asymptotic approximations for the number of fanout-free functions</a>, IEEE Trans. Computers, 27 (1978), 1180-1183. (Annotated scanned copy) %H A005616 J. T. Butler, Letter to N. J. A. Sloane, <a href="/A006447/a006447.pdf">Jun. 1975</a> and <a href="/A005607/a005607_1.pdf">Dec. 1978</a>. %H A005616 J. T. Butler, <a href="http://dx.doi.org/10.1109/T-C.1975.224288">On the number of functions realized by cascades and disjunctive networks</a>, IEEE Trans. Computers, C-24 (1975), 681-690. (<a href="/A005613/a005613.pdf">Annotated scanned copy</a>) %H A005616 K. L. Kodandapani and S. C. Seth, <a href="http://doi.ieeecomputersociety.org/10.1109/TC.1978.1675103">On combinational networks with restricted fan-out</a>, IEEE Trans. Computers, 27 (1978), 309-318. (<a href="/A005736/a005736.pdf">Annotated scanned copy</a>) %F A005616 From _Andrew Howroyd_, Apr 03 2025: (Start) %F A005616 E.g.f.: 2*(p + q + 1) where p,q satisfy q = exp(p) - p - 1, p = exp(2*q + p + x) - (2*q + p + 1). %F A005616 E.g.f.: 2*exp( Series_Reversion(x + log(2*exp(x)-1) - 2*(exp(x) - 1)) ). %F A005616 E.g.f.: 2 + 2*Series_Reversion(log(1 + 3*x + 2*x^2) - 2*x). (End) %o A005616 (PARI) seq(n)=my(p=2*exp(x + O(x*x^n)), g=serreverse(x + log(p-1) - p + 2)); Vec(serlaplace(2*exp(g))) \\ _Andrew Howroyd_, Apr 03 2025 %o A005616 (PARI) seq(n)=Vec(2*serlaplace(1 + serreverse(log(1 + 3*x + 2*x^2 + O(x*x^n)) - 2*x))) \\ _Andrew Howroyd_, Apr 03 2025 %Y A005616 Cf. A005738, A005739. %K A005616 nonn %O A005616 0,1 %A A005616 _N. J. A. Sloane_ %E A005616 a(0), a(14)-a(16) from _Sean A. Irvine_, Jul 21 2016