cp's OEIS Frontend

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.

A076541 a(n) = Sum_{k=1..n} C(n,k) mod k.

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%I A076541 #18 Apr 26 2025 03:27:33
%S A076541 0,1,2,2,3,8,9,11,6,13,14,26,27,28,32,46,47,49,50,68,81,82,83,116,102,
%T A076541 101,105,105,106,142,143,143,153,172,165,222,223,216,259,278,279,256,
%U A076541 257,327,394,295,296,422,374,318,328,384,385,420,469,461,465,450,451
%N A076541 a(n) = Sum_{k=1..n} C(n,k) mod k.
%H A076541 Amiram Eldar, <a href="/A076541/b076541.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2500 from Paolo P. Lava)
%H A076541 Amiram Eldar, <a href="/A076541/a076541.jpg">Plot of a(n)/n^2 for n = 1..10^4</a>.
%F A076541 a(n) seems to be asymptotic to c*n^2 with c around 0.18...
%t A076541 a[n_] := Sum[Mod[Binomial[n, k], k], {k, 1, n}]; Array[a, 60] (* _Amiram Eldar_, Apr 26 2025 *)
%o A076541 (PARI) a(n)=sum(k=1,n,binomial(n,k)%k)
%Y A076541 Row sums of A081371.
%K A076541 nonn
%O A076541 1,3
%A A076541 _Benoit Cloitre_, Oct 19 2002