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.

A060644 a(n) = floor((n+1)^(n+1)/n^n).

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%I A060644 #21 Oct 12 2024 21:34:03
%S A060644 1,4,6,9,12,14,17,20,23,25,28,31,33,36,39,42,44,47,50,53,55,58,61,63,
%T A060644 66,69,72,74,77,80,82,85,88,91,93,96,99,101,104,107,110,112,115,118,
%U A060644 120,123,126,129,131,134,137,139,142,145,148,150,153,156,159,161,164
%N A060644 a(n) = floor((n+1)^(n+1)/n^n).
%C A060644 a(n) = floor(1/R) where R is the radius of convergence of the series S(x,n) = Sum_{k>=0} binomial(n*k, k)*x^k. - _Michel Lagneau_, Mar 09 2011
%H A060644 Paolo Xausa, <a href="/A060644/b060644.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Harry J. Smith).
%F A060644 a(n) = A000312(n+1)/A000312(n) = floor(e*(n+1/2)) at least for terms shown.
%e A060644 a(7) = floor(8^8/7^7) = floor(16777216/823543) = floor(20.37...) = 20.
%t A060644 A060644[n_] := If[n == 0, 1, Floor[(n+1)^(n+1)/n^n]]; Array[A060644, 100, 0] (* _Paolo Xausa_, Oct 12 2024 *)
%o A060644 (PARI) { for (n=0, 1000, write("b060644.txt", n, " ", floor((n + 1)^(n + 1)/n^n)); ) } \\ _Harry J. Smith_, Jul 09 2009
%K A060644 nonn
%O A060644 0,2
%A A060644 _Henry Bottomley_, Apr 17 2001