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 A378302 #22 May 02 2025 08:12:28
%S A378302 0,2,2,58,12618,601016690,1832624137336299922,
%T A378302 23951146041928082853307218802404658090,
%U A378302 5768658823449206338089748357862286887548602533639737369730665340966207267034
%N A378302 Number of nondegenerate balanced Boolean functions of n variables.
%C A378302 A Boolean function is degenerate on some variable if its output does not depend on the variable, and it is said to be non-degenerate if it is not degenerate on any variable.
%H A378302 Aniruddha Biswas and Palash Sarkar, <a href="https://arxiv.org/abs/2304.14069">Counting unate and balanced monotone Boolean functions</a>, arXiv:2304.14069 [math.CO], 2023.
%H A378302 Aniruddha Biswas and Palash Sarkar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Biswas/biswas6.html">Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy</a>, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 6.
%F A378302 a(n) = Sum_{i=1..n} (-1)^(n-i) * binomial(n,i) * binomial(2^i,2^(i-1)).
%t A378302 a[n_]:=Sum[(-1)^(n-i)*Binomial[n,i]*Binomial[2^i,2^(i-1)],{i,n}]; Array[a,9,0] (* _Stefano Spezia_, Nov 24 2024 *)
%o A378302 (Python)
%o A378302 from math import comb
%o A378302 def A378302(n): return sum(-comb(n,i)*comb(1<<n-i,1<<n-i-1) if i&1 else comb(n,i)*comb(1<<n-i,1<<n-i-1) for i in range(n)) # _Chai Wah Wu_, Dec 11 2024
%Y A378302 Cf. A037293, A000618.
%K A378302 nonn,easy
%O A378302 0,2
%A A378302 _Aniruddha Biswas_, Nov 22 2024