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.

A003723 E.g.f. exp(tanh(x)).

This page as a plain text file.
%I A003723 M4327 #29 Jan 27 2018 18:19:57
%S A003723 1,1,1,-1,-7,-3,97,275,-2063,-15015,53409,968167,-752343,-77000363,
%T A003723 -166831871,7433044411,43685848289,-843598411471,-9398558916159,
%U A003723 107426835190735,2116926930779225,-14072980460605907
%N A003723 E.g.f. exp(tanh(x)).
%C A003723 Row sums of triangle A111593.
%D A003723 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003723 T. D. Noe, <a href="/A003723/b003723.txt">Table of n, a(n) for n = 0..100</a>
%F A003723 a(n) := sum(m=1..n, sum(k=m..n, binomial(k-1,m-1)*k!*(-1)^(m+k)*2^(n-k)*Stirling2(n,k))/m!), n>0, a(0)=1. - _Vladimir Kruchinin_, Jun 28 2011
%t A003723 With[{nn = 30}, CoefficientList[Series[Exp[Tanh[x]], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Apr 11 2014 *)
%o A003723 (Maxima)
%o A003723 a(n):=if n=0 then 1 else sum(sum(binomial(k-1,m-1)*k!*(-1)^(m+k)*2^(n-k)*stirling2(n,k),k,m,n)/m!,m,1,n); /* _Vladimir Kruchinin_, Jun 28 2011 */
%Y A003723 Cf. A003706, A003710.
%K A003723 sign
%O A003723 0,5
%A A003723 _R. H. Hardin_, _Simon Plouffe_