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.

A009238 Expansion of e.g.f. exp(tan(sin(x))).

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%I A009238 #27 Jan 27 2018 06:30:28
%S A009238 1,1,1,2,5,8,13,-64,-855,-5632,-38791,-205184,-747539,-240640,
%T A009238 59637061,859820032,9421489105,90170851328,573991066225,1502445600768,
%U A009238 -49290541346219,-1320541298393088,-20481513828195331,-272882319216148480
%N A009238 Expansion of e.g.f. exp(tan(sin(x))).
%F A009238 a(n) = Sum(m=1..n, Sum(k=m..n, (((-1)^(k-m)+1)*(Sum(j=m..k, C(j-1,m-1)*j! *2^(k-j-1) *Stirling2(k,j)*(-1)^((m+k)/2+j)))*((-1)^(n-k)+1)*Sum(i=0..k/2, (2*i-k)^n *C(k,i)*(-1)^((n+k)/2-i)))/(2^k*k!))/m!). - _Vladimir Kruchinin_, May 05 2011
%t A009238 With[{nn=30},CoefficientList[Series[Exp[Tan[Sin[x]]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 25 2011 *)
%o A009238 (Maxima)
%o A009238 a(n):=sum(sum((((-1)^(k-m)+1)*(sum(binomial(j-1,m-1)*j!*2^(k-j-1) *stirling2(k,j)*(-1)^((m+k)/2+j),j,m,k))*((-1)^(n-k)+1)*sum((2*i-k)^n *binomial(k,i)*(-1)^((n+k)/2-i),i,0,k/2))/(2^k*k!),k,m,n)/m!,m,1,n); /* _Vladimir Kruchinin_, May 05 2011 */
%o A009238 (PARI)
%o A009238 x='x+O('x^66); /* that many terms */
%o A009238 egf=exp(tan(sin(x))); /* = 1 + x + 1/2*x^2 + 1/3*x^3 + 5/24*x^4 + ... */
%o A009238 Vec(serlaplace(egf)) /* show terms */ /* _Joerg Arndt_, May 05 2011 */
%K A009238 sign,easy
%O A009238 0,4
%A A009238 _R. H. Hardin_
%E A009238 Extended with signs by _Olivier Gérard_, Mar 15 1997
%E A009238 Definition corrected by _Joerg Arndt_, May 05 2011