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.

A087301 a(n) = n!*Sum_{i=1..n-1} (-1)^(i+1)/i.

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%I A087301 #12 Jul 01 2018 09:20:29
%S A087301 2,3,20,70,564,3108,30624,230256,2705760,25771680,352805760,
%T A087301 4067556480,63651813120,861371884800,15176802816000,235775183616000,
%U A087301 4620563523072000,81032645804544000,1748700390205440000
%N A087301 a(n) = n!*Sum_{i=1..n-1} (-1)^(i+1)/i.
%C A087301 Stirling transform of A052882(n)=[0,2,9,52,375,...] is a(n+1)=[0,2,3,20,...]. - _Michael Somos_, Mar 04 2004
%F A087301 E.g.f.: x*log(1+x)/(1-x). a(n) = 1/2*(-1)^n*n!*(2*(-1)^n*log(2)+Psi(1/2+1/2*n)-Psi(1/2*n)).
%F A087301 a(n) ~ n! * log(2). - _Vaclav Kotesovec_, Jul 01 2018
%t A087301 Rest[Table[n!Sum[(-1)^(i+1)/i,{i,n-1}],{n,20}]] (* _Harvey P. Dale_, Oct 24 2011 *)
%o A087301 (PARI) a(n)=if(n<0,0,n!*polcoeff(log(1+x+x*O(x^n))*x/(1-x),n))
%Y A087301 Cf. A024167, A052881.
%K A087301 nonn
%O A087301 2,1
%A A087301 _Vladeta Jovovic_, Oct 20 2003