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.

A009633 E.g.f. tan(cos(x)*x) (odd powers only).

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%I A009633 #18 Sep 24 2019 10:38:11
%S A009633 1,-1,-39,55,39697,-2289,-235548247,-1367615353,4617417380769,
%T A009633 85802560805023,-226896487004217095,-9332987296855749801,
%U A009633 23509703520941274769841,1792438008018628579394735
%N A009633 E.g.f. tan(cos(x)*x) (odd powers only).
%F A009633 a(n)=sum(k=0..n, binomial(2*n+1,2*k+1)*(sum(i=0..k,(2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i)))*(sum(j=1..2*k+1, j!*2^(1-j)*(-1)^(n+1+j)*stirling2(2*k+1,j)))). - _Vladimir Kruchinin_, Jun 18 2011
%t A009633 terms = 14;
%t A009633 egf = Tan[Cos[x]*x] + O[x]^(2 terms);
%t A009633 Partition[ CoefficientList[egf, x] Range[0, 2 terms - 1]!, 2][[All, 2]] (* _Jean-François Alcover_, Sep 24 2019 *)
%o A009633 (Maxima)
%o A009633 a(n):=sum(binomial(2*n+1,2*k+1)*(sum((2*k+1-2*i)^(2*n-2*k)*binomial(2*k+1,i),i,0,k))*(sum(j!*2^(1-j)*(-1)^(n+1+j)*stirling2(2*k+1,j),j,1,2*k+1)),k,0,n); /* _Vladimir Kruchinin_, Jun 18 2011 */
%K A009633 sign
%O A009633 0,3
%A A009633 _R. H. Hardin_
%E A009633 Extended with signs by _Olivier Gérard_, Mar 15 1997