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 A172320 #8 Mar 28 2025 11:29:53 %S A172320 1,2,4,8,16,32,64,128,256,512,1024,2047,4092,8180,16352,32688,65344, %T A172320 130624,261120,521984,1043456,2085888,4169729,8335366,16662552, %U A172320 33308752,66584816,133104288,266077952,531894784,1063267584 %N A172320 11th column of A172119. %H A172320 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,0,0,0,0,0,0,0,-1). %F A172320 a(n)=sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))) with k=10. %F A172320 G.f: f(z)=1/(1-2*z+z^(11)). %F A172320 a(n+11)=2*a(n+10)-a(n). %e A172320 a(12)=C(12,12)*2^12-C(2,1)*2^1=4092. %p A172320 k:=10:taylor(1/(1-2*z+z^(k+1)),z=0,30); for k from 0 to 20 do for n from 0 to 30 do b(n):=sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))):od:k: seq(b(n),n=0..30):od; %Y A172320 Cf. A172319, A172318, A172317, A172316, A172119, A001949, A107066. %Y A172320 Partial sums of A122265. %K A172320 easy,nonn %O A172320 0,2 %A A172320 _Richard Choulet_, Jan 31 2010