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 A101510 #35 Mar 19 2019 04:17:11
%S A101510 1,2,5,10,21,43,87,175,352,707,1417,2836,5674,11353,22716,45443,90886,
%T A101510 181748,363451,726870,1453773,2907648,5815315,11630195,23259059,
%U A101510 46515887,93029852,186060921,372129424,744272221,1488552317,2977079872
%N A101510 Diagonal sums of binomial-Möbius product.
%C A101510 Diagonal sums of A101508.
%H A101510 Seiichi Manyama, <a href="/A101510/b101510.txt">Table of n, a(n) for n = 0..500</a>
%F A101510 a(n) = Sum_{k=0..floor(n/2)} Sum_{i=0..n-k, (k+1)|(i+1)} binomial(n-k,i).
%F A101510 G.f.: (1/x^2) * Sum_{n>=1} a*z^n/(1-a*z^n) (generalized Lambert series) where z=x/(1-x) and a=x. - _Joerg Arndt_, Jan 30 2011
%F A101510 a(n) ~ log(2) * 2^(n+1). - _Vaclav Kotesovec_, Mar 18 2019
%t A101510 a[n_] := Sum[If[Mod[i+1, k+1] == 0, Binomial[n-k, i], 0], {k, 0, n/2}, {i, 0, n-k}]; Table[a[n], {n, 0, 31}] (* _Jean-François Alcover_, Jan 24 2014 *)
%t A101510 nmax = 40; CoefficientList[Series[(1/x^2) * Sum[x*(x/(1-x))^k/(1-x*(x/(1-x))^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 18 2019 *)
%o A101510 (PARI) a(n) = sum(k=0, n\2, sum(i=0, n-k, if (!Mod(i+1, k+1), binomial(n-k, i)))); \\ _Michel Marcus_, Mar 16 2019
%K A101510 easy,nonn
%O A101510 0,2
%A A101510 _Paul Barry_, Dec 05 2004