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 A275012 #33 Jun 06 2021 09:05:57 %S A275012 1,1,4,11,29,69,174,413,995,2364,5581,13082,30600,71111,164660,379682, %T A275012 872749 %N A275012 Number of nonzero coefficients in the polynomial factor of the expression counting binomial coefficients with 2-adic valuation n. %H A275012 Eric Rowland, <a href="https://dx.doi.org/10.1007/978-3-319-62809-7_3">Binomial Coefficients, Valuations, and Words</a>, In: Charlier É., Leroy J., Rigo M. (eds) Developments in Language Theory, DLT 2017, Lecture Notes in Computer Science, vol 10396. %H A275012 Lukas Spiegelhofer and Michael Wallner, <a href="https://arxiv.org/abs/1604.07089">An explicit generating function arising in counting binomial coefficients divisible by powers of primes</a>, arXiv:1604.07089 [math.NT], 2016. %H A275012 Lukas Spiegelhofer and Michael Wallner, <a href="https://arxiv.org/abs/1710.10884">Divisibility of binomial coefficients by powers of two</a>, arXiv:1710.10884 [math.NT], 2017. %e A275012 For n=2, the number of integers m such that binomial(k,m) is divisible by 2^n but not by 2^(n+1) is given by 2^X_1 (-1/8 X_10 + 1/8 X_10^2 + X_100 + 1/4 X_110), where X_w is the number of occurrences of the word w in the binary representation of k. The polynomial factor of this expression has a(2) = 4 nonzero terms. - _Eric Rowland_, Mar 05 2017 %Y A275012 A001316, A163000, and A163577 count binomial coefficients with 2-adic valuation 0, 1, and 2. - _Eric Rowland_, Mar 15 2017 %K A275012 nonn,more %O A275012 0,3 %A A275012 _Michel Marcus_, Nov 12 2016 %E A275012 a(12)-a(16) from _Eric Rowland_, Mar 20 2017